Statistics Questions

PRACTICE ANOTHER A paper summarizes data from 61 young children living in a particular county in a particular state who had their blood lead levels measured as part of a routine healthcare visit The sample mean blood level was 16 g dL and the sample standard deviation was 6 7 g dL Suppose that it is reasonable to regard this sample as representative of young children living in this county Do these data provide convincing evidence that the mean blood lead level for young children in this county is greater than 10 g dL Carry out a hypothesis test using a 0 01 Hint See Example 12 11 USE SALT State the appropriate null and alternative hypotheses in g dL Enter for as needed Ho H Find the test statistic Round your answer to two decimal places Use technology to find the P value Round your answer to four decimal places P value State the conclusion in the problem context Reject Ho We do not have convincing evidence that the mean blood lead level for young children in this county is greater than 10 g dL Fail to reject Ho We do not have convincing evidence that the mean blood lead level for young children in this county is greater than 10 g dL Fail to reject H We have convincing evidence that the mean blood lead level for young children in this county is greater than 10 g dL Reject Ho We have convincing evidence that the mean blood lead level for young children in this county is greater than 10 g dL

1 Points DETAILS PECKSTAT3 12 2 032 MI S USE SALT MY NOTES A manufacturer of college textbooks is interested in estimating the strength of the bindings produced by a particular binding machine Strength can be measured by recording the force req the pages of a book from its binding books PRACTICE A f this force is measured in pounds what is the minimum number of books that should be tested to estimate the average force required to break the binding with a margin of error of 0 1 5 confidence Assume that a is known to be 0 9 pounds Round your answer up to the nearest integer

A report about how American college students manage their finances includes data from a survey of college students Each person in a representative sample of 793 college students was asked if they had one or more credit cards and if so whether they paid their balance in full each month There were 500 who paid in full each month For this sample of 500 students the sample mean credit card balance was reported to be 825 The sample standard deviation of the credit card balances for these 500 students was not reported but for purposes of this exercise suppose that it was 205 Is there convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than 905 the value reported for all college students with credit cards Carry out a hypothesis test using a significance level of 0 01 LUSE SALT State the appropriate null and alternative hypotheses in dollars Enter for as needed Ho H Find the test statistic Round your answer to two decimal places Use technology to find the P value Round your answer to four decimal places P value State the conclusion in the problem context We reject Ho We do not have convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than 905 We fail to reject Ho We do not have convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than 905 We fail to reject Ho We have convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than 905 We reject H We have convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than 905

An article describes surveys of representative samples of rural and urban adult Americans Of 527 urban adults 197 reported that they use the Internet almost constantly In the sample of 285 rural adults 61 reported that they use the Internet almost constantly LUSE SALT Construct a 99 confidence interval for the difference in the proportion who report using the Internet almost constantly for urban and rural adult Americans Use Urban Rural Enter your answer using interval notation Round your numerical values to four decimal places Interpret the interval We are 99 confident that the true difference in the proportion of urban adults who use the Internet almost constantly and the same proportion for rural adults falls Select this interval The bounds of the interval suggest the Select Submit Answer DETAILS PREVIOUS ANSWERS USE SALT PECKSTAT3 11 1 010 S O 3 3 11 Points Many people believe that they experience information overload in today s digital world A report describes a survey in which people were asked if they feel overloaded by information Suppose in a representative sample of 634 college graduates 101 indicated that they suffered from information overload while 118 people in an independent representative sample of 496 people who had never attended college said that they suffered from information overload MY NOTES 2 Construct a 95 large sample confidence interval for the proportion of college graduates who experience information overload Hint This is a one sample confidence interval Enter your answer

4 The formula used to calculate a confidence interval for the mean of a normal population is x t critical value What is the appropriate t critical value for each of the following confidence levels and sample sizes Round your answers to two decimal places a 90 confidence n 16 USE SALT b 90 confidence n 23 c 95 confidence n 11 vn Need Help Read It Submit Answer

TICE ANOTHER Students in a representative sample of 69 second year students selected from a large university in England participated in a study of academic procrastination Each student in the sample completed the Tuckman Procrastination Scale which measures procrastination tendencies Scores on this scale can range from 16 to 64 with scores over 40 indicating higher levels of procrastination For the 69 second year students in the study at the university the sample mean procrastination score was 41 00 and the sample standard deviation was 6 85 USE SALT a Construct a 95 confidence interval estimate of the population mean procrastination scale for second year students at this college Enter your answer using interval notation Round your numerical values to three decimal places b How does the confidence interval for the population mean score for second year students compare to the confidence interval for first year students of 35 472 38 668 What does this tell you about the difference between first year and second year students in terms of mean procrastination score The confidence interval for second year students overlaps the confidence interval for first year students Therefore it seems plausible that second year students tend to procrastinate less than first year students at this university The confidence interval for second year students does not overlap and has values that are entirely below the confidence interval for first year students Therefore it seems plausible that second year students tend to procrastinate about the same as first year students at this university The confidence interval for second year students does not overlap and has values that are entirely below the confidence interval for first year students Therefore it seems plausible that second year students tend to procrastinate less than first year students at this university The confidence interval for second year students overlaps the confidence interval for first year students Therefore it seems plausible that second year students tend to procrastinate about the same as first year students at this university The confidence interval for second year students does not overlap and has values that are entirely above the confidence interval for first year students Therefore it seems plausible that second year students tend to procrastinate more than first year students at this university Watch it

W Chapter 11 Quiz MATH1123 section OB Fall 2023 WebAssign A report summarizes a survey of people in two independent random samples One sample consisted of 600 young adults age 19 to 35 and the other sample consisted of 200 parents of young adults age 19 to 35 The young adults were presented with a variety of situations such as getting married or buying a house and were asked if they thought that their parents were likely to provide financial support in that situation The parents of young adults were presented with the same situations and asked if they would be likely to provide financial support to their child in that situation The report stated that the proportion of young adults who thought their parents would help with buying a house or renting an apartment for the sample of young adults was 0 37 For the sample of parents the proportion who said they would help with buying a house or renting an apartment was 0 27 Based on these data can you conclude that the proportion of parents who say they would help with buying a house or renting an apartment is significantly less than the proportion of young adults who think that their parents would help Test the appropriate hypotheses using a significance level of 0 05 Let p be the proportion of all parents of young adults who say they would help with buying a house or renting an apartment and p2 be the proportion of young adults who think that their parents would help State the appropriate null and alternative hypotheses Ho P P 0 Ha P P 0 Ho P P 0 Ha P P 0 Ho P Ha P Ho P H P Z P value USE SALT P 0 P 0 P 0 Ho P P 0 H P P 0 Find the test statistic and P value Use a table or SALT Round your test statistic to two decimal places and your P value to four decimal places P 0 State your conclusion We fail to reject Ho We do not have convincing evidence that the proportion of parents who say they would help with buying a house or apartment is less than the proportion of young adults who think that their parents would help We reject Ho We have convincing evidence that the proportion of parents who say they would help with buying a house or apartment is less than the proportion of young adults who think that their parents would help We reject H We do not have convincing evidence that the proportion of parents who say they would help with buying a house or apartment is less than the proportion of young adults who think

A report summarizes data from independent representative samples of approximately 1 000 people in each of 28 different countries The report asked people if they thought that in general teachers in their country were trustworthy or untrustworthy In the sample from the United States 59 responded trustworthy In the sample from Canada 64 responded trustworthy For this exercise assume that the two sample sizes were 1 000 Based on these data can you conclude that the proportion of people in the United States who think that teachers in their country are trustworthy is less than this proportion for people in Canada Use 0 05 Let p be the population proportion of people in the United States who think their teachers are trustworthy and p be the population proportion of people in Canada who think their teachers are trustworthy LUSE SALT State the appropriate null and alternative hypotheses Enter for as needed Ho H Find the test statistic Round your answer to two decimal places MY NOTES Use technology to find the P value Round your answer to four decimal places P value State your conclusion Fail to reject Ho We have convincing evidence that the proportion of people in the United States who think that teachers in their country are trustworthy is less than this proportion for people in Canada Fail to reject Ho We do not have convincing evidence that the proportion of people in the United States who think that teachers in their country are trustworthy is less than this proportion for people in Canada Reject Ho We do not have convincing evidence that the proportion of people in the United States who think that teachers in their country are trustworthy is less than this proportion for people in Canada Reject Ho We have convincing evidence that the proportion of people in the United States who think that teachers in their country are trustworthy is less than this proportion for people in Canada

MY NOTES Many people believe that they experience information overload in today s digital world A report describes a survey in which people were asked if they feel overloaded by information Suppose in a representative sample of 634 college graduates 101 indicated that they suffered from information overload while 118 people in an independent representative sample of 496 people who had never attended college said that they suffered from information overload LUSE SALT a Construct a 95 large sample confidence interval for the proportion of college graduates who experience information overload Hint This is a one sample confidence interval Enter your answer using interval notation Round your numerical values to four decimal places Interpret the interval There is a 95 chance that the true proportion of college graduates who experience information overload falls directly in the middle of this interval O We are 95 confident that the true difference in the proportion of college graduates who experience information overload and this proportion for people who have never attended college falls within this interval There is a 95 chance that the true difference in the proportion of college graduates who experience information overload and this proportion for people who have never attended college falls directly in the middle of this interval We are 95 confident that the true proportion of college graduates who experience information overload falls within this interval We are 95 confident that the true proportion of people who have never attended college who experience information overload falls within this interval b Construct a 95 large sample confidence interval for the proportion of people who have never attended college who experience information overload Enter your answer using interval notation Round your numerical values to four decimal places Interpret the interval There is a 95 chance that the true proportion of college graduates who experience information overload falls directly in the middle of this interval We are 95 confident that the true difference in the proportion of college graduates who experience information overload and this proportion for people who have never attended college falls within this interval There is a 95 chance that the true difference in the proportion of college graduates who experience information overload and this proportion for people who have never attended college falls directly in the middle of this interval We are 95 confident that the true proportion of college graduates who experience information overload falls within this interval

Suppose an article states People ages 35 to 54 were the least likely group to report buckling up in the back seat Seventy four percent of this group reported always buckling up in the back seat compared with 78 of adults age 18 to 34 Suppose that it is reasonable to regard the sample of people 18 to 34 years old and the sample of people of age 35 to 54 as independent samples that are representative of these two age groups and that both sample sizes were 50 Is there convincing evidence that the proportion who always buckle up in the back seat is different for people of age 18 to 34 and people of age 35 to 54 Test the appropriate hypotheses using a significance level of 0 05 Let p be the population proportion of people age 18 to 34 who always buckle up in the back seat and p be the population proportion of people age 35 to 54 who always buckle up in the back seat LUSE SALT State the appropriate null and alternative hypotheses Enter for as needed Ho H Find the test statistic Round your answer to two decimal places Use technology to find the P value Round your answer to four decimal places P value State your conclusion Reject Ho We have convincing evidence that the proportion who always buckle up in the back seat is different for people of age 18 to 34 and people of age 35 to 54 Reject Ho We do not have convincing evidence that the proportion who always buckle up in the back seat is different for people of age 18 to 34 and people of age 35 to 54 Fail to reject Ho We do not have convincing evidence that the proportion who always buckle up in the back seat is different for people of age 18 to 34 and people of age 35 to 54 Fail to reject Ho We have convincing evidence that the proportion who always buckle up in the back seat is different for people of age 18 to 34 and people of age 35 to 54

A company surveyed adult Americans about their consumer debt They reported that 48 of Millennials those born between 1981 and 1996 and 59 of Gen Xers those born between 1965 and 1980 did not pay off their credit cards each month and therefore carried a balance from month to month Suppose that these percentages were based on representative samples of 450 Millennials and 300 Gen Xers Is there convincing evidence that the proportion of Gen Xers who do not pay off their credit cards each month is greater than this proportion for Millennials Test the appropriate hypotheses using a significance level of 0 05 Let p be the proportion of Gen Xers who do not pay off their credit cards each month and p be the proportion of Millennials who do not pay off their credit cards each month USE SALT State the appropriate null and alternative hypotheses Enter for as needed Ho H Find the test statistic Round your answer to two decimal places MY NOTES Use technology to find the p value Round your answer to four decimal places p value PRACTICE ANOTHER State your conclusion We fail to reject Ho We have convincing evidence that the proportion of Gen Xers who do not pay off their credit cards each month is greater than this proportion for Millennials We reject Ho We do not have convincing evidence that the proportion of Gen Xers who do not pay off their credit cards each month is greater than this proportion for Millennials We reject Ho We have convincing evidence that the proportion of Gen Xers who do not pay off their credit cards each month is greater than this proportion for Millennials We fail to reject Ho We do not have convincing evidence that the proportion of Gen Xers who do not pay off their credit cards each month is greater than this proportion for Millennials

A report on food science states that younger adults are more likely to see foods with genetically modified ingredients as being bad for their health than older adults This statement is based on a representative sample of 175 adult Americans age 18 to 29 and a representative sample of 450 adult Americans age 50 to 64 Of those in the 18 to 29 age group 48 said they believed these foods were bad for their health while only 36 of those in the 50 to 64 age group believed this USE SALT a Are the sample sizes large enough to use the large sample confidence interval to estimate the difference in the population proportions Explain Let p 0 48 and p 0 36 n 175 and n 450 where the 1 subscript indicates the age 18 29 group and the 2 subscript indicates the age 50 64 group Since n p n P and n 1 B all at least 10 the sample sizes are 7 p are sample confidence interval b Estimate the difference in the proportion of adult Americans age 18 to 29 who believe the foods made with genetically modified ingredients are bad for their health and the corresponding proportion for adult Americans age 50 to 64 Use a 90 confidence interval Use p P Enter your answer using interval notation Round your numerical values to four decimal places c Is zero in the confidence interval Yes o No 8 large enough to use the large What does this suggest about the difference in the two population proportions It is not plausible that the two population proportions are equal but it is unclear which proportion is higher It is highly likely that the true proportion is higher for adult Americans age 18 to 29 OIt is plausible that the two population proportions could be equal OIt is highly likely that the true proportion is higher for adult Americans age 50 to 64

Chapter 11 Homework MATH1123 section OB Fall 2023 WebAssign Suppose that in studies of mobile phone use while driving conducted in 2015 and 2020 3 2 of the drivers observed in 2015 and 2 6 of the drivers observed in 2020 were using a handheld mobile phone while driving Suppose that these percentages were based on observations from independent random samples of 1 500 drivers in 2015 and 1 500 drivers in 2020 a Are the sample sizes large enough to use the large sample confidence interval for a difference in population proportions Yes O No USE SALT b Assume that it is reasonable to regard these samples as representative of drivers in 2015 and drivers in 2020 Estimate the difference in the proportion of drivers in 2015 and the proportion of drivers in 2020 who use a mobile phone while driving using a 95 confidence interval Use 2015 Drivers 2020 Drivers Enter your answer using interval notation Round your numerical values to four decimal places c Is 0 included in the confidence interval Yes No What does this suggest about the difference in proportions for 2015 and 2020 O It is plausible that the two population proportions could be equal It is not plausible that the two population proportions could be equal d Interpret the confidence interval in the context of this problem We are 95 confident A that the true difference in the proportion of drivers in 2015 who used a handheld mobile phone while driving and the same proportion for drivers in 2020 falls

Suppose a report summarizes data from independent representative samples of approximately 1 000 people in each of 28 different countries People in the samples were asked if they thought that in general scientists in their country were trustworthy or untrustworthy In the sample from the United States 63 responded trustworthy In the sample from Canada 66 responded trustworthy For this exercise assume that the two sample sizes were 1 000 Carry out a hypothesis test to determine if there is convincing evidence that the proportion of people who think that in general scientists in their country are trustworthy differs for the United States and Canada Use a 0 05 Let p be the population proportion of people in the United States who think their scientists are trustworthy and be the population proportion of people in Canada who think their scientists are trustworthy P2 USE SALT State the appropriate null and alternative hypotheses Enter for as needed Ho H Find the test statistic Round your answer to two decimal places Use technology to find the P value Round your answer to four decimal places P value MY NOTES PRACTICE ANOTHER State your conclusion Fail to reject Ho We have convincing evidence that the proportion of people who think that in general scientists in their country are trustworthy differs for the United States and Canada Reject Ho We have convincing evidence that the proportion of people who think that in general scientists in their country are trustworthy differs for the United States and Canada Reject Ho We do not have convincing evidence that the proportion of people who think that in general scientists in their country are trustworthy differs for the United States and Canada t Fail to reject Ho We do not have convincing evidence that the proportion of people who think that in general scientists in their country are trustworthy differs for the United States and Canada

If the correlation coefficient and standard deviations are given find the line of best fit and find estimates for x given y and for y given x

5 The diameter of chocolate chip cookies from a local bakery are normally distributed with an average diameter of 4 inches and a variance 2 25 Would a chocolate chip cookie from this local baker with a diameter of 8 inches be very unusual for this bakery Why or why not

If an initial principal P is invested at an annual rater and the interest is compounded n times per year the amount A in the account after t years is A P 1 1 On May 31 2009 the Annual Percentage Rate listed at Jeff s bank for regular savings accounts was 0 15 compounded monthly Use the equation above to answer the following a If P 2000 what is A 6 Round your answer to the nearest cent Ad b Using the principal from part a solve the equation A t 4000 for t Round your answer to two decimal places t c What principal P should be invested so that the account balance is 2000 in three years Round your answer to the nearest cent P

Three years ago the mean price of an existing single family home was 243 718 A real estate broker believes tha existing home prices in her neighborhood are higher a State the null and alternative hypotheses in words b State the null and alternative hypotheses symbolically c Explain what it would mean to make a Type I error d Explain what it would mean to make a Type II error a State the null hypothesis in words Choose the correct answer below OA The mean price of a single family home in the broker s neighborhood is greater than 243 718 OB The mean price of a single family home in the broker s neighborhood is different from 243 718 OC The mean price of a single family home in any neighborhood is 243 718 D The mean price of a single family home in the broker s neighborhood is 243 718 State the alternative hypothesis in words Choose the correct answer below OA The mean price of a single family home in the broker s neighborhood is different from 243 718 B The mean price of a single family home in any neighborhood is 243 718 C The mean price of a single family home in the broker s neighborhood is greater than 243 718 D The mean price of a single family home in the broker s neighborhood is 243 718 b State the hypotheses symbolically Ho H

For students who first enrolled in two year public institutions in a recent semester the proportion who earned a bachelor s degree within six years was 0 399 The president of a certain junior college believes that the proportion of students who enroll in her institution have a higher completion rate a State the null and alternative hypotheses in words b State the null and alternative hypotheses symbolically c Explain what it would mean to make a Type I error d Explain what it would mean to make a Type II error a State the null hypothesis in words Choose the correct answer below OA Among students who first enroll in two year public institutions the completion rate is 0 399 B Among students who enroll at the certain junior college the completion rate is 0 399 OC Among students who enroll at the certain junior college the completion rate is less than 0 399 OD Among students who enroll at the certain junior college the completion rate is greater than 0 399 State the alternative hypothesis in words Choose the correct answer below A Among students who enroll at the certain junior college the completion rate is greater than 0 399 OB Among students who first enroll in two year public institutions the completion rate is 0 399 OC Among students who enroll at the certain junior college the completion rate is 0 399 OD Among students who enroll at the certain junior college the completion rate is less than 0 399 b State the hypotheses symbolically Ho

Three years ago the mean price of an existing single family home was 243 718 A real estate broker believes that existing home prices in her neighborhood are higher a State the null and alternative hypotheses in words b State the null and alternative hypotheses symbolically c Explain what it would mean to make a Type I error d Explain what it would mean to make a Type II error a State the null hypothesis in words Choose the correct answer below OA The mean price of a single family home in the broker s neighborhood is greater than 243 718 OB The mean price of a single family home in the broker s neighborhood is different from 243 718 OC The mean price of a single family home in any neighborhood is 243 718 D The mean price of a single family home in the broker s neighborhood is 243 718 State the alternative hypothesis in words Choose the correct answer below OA The mean price of a single family home in the broker s neighborhood is different from 243 718 OB The mean price of a single family home in any neighborhood is 243 718 OC The mean price of a single family home in the broker s neighborhood is greater than 243 718 OD The mean price of a single family home in the broker s neighborhood is 243 718

appropriate apper An official of a large national union claims that the fraction of women in the union is not significantly different from one half Using the critical value approach and the sample inform below carry out a test of this statement Let a 0 05 Ho sample size H women men 400 167 State the null and alternative hypotheses Enter for as needed 233 Find the value of the test statistic 3 3 Determine the critical value s for this test Round your answer s to two decimal places If the test is one tailed enter NONE for the unused tail test statistic 1 96 test statistic 2 1 96 X State your conclusion Reject Ho There is sufficient evidence to conclude that the fraction of women in the union is significantly different from one half O Reject Ho There is insufficient evidence to conclude that the fraction of women in the union is significantly different from one half O Do not reject Ho There is sufficient evidence to conclude that the fraction of women in the union is significantly different from one half O Do not reject Ho There is insufficient evidence to conclude that the fraction of women in the union is significantly different from one half

Fill in the blank to complete the statement If we do not reject the null hypothesis when the statement in the alternative hypothesis is true we have made a Type error If we do not reject the null hypothesis when the statement in the alternative hypothesis is true we have made a Type error

For students who first enrolled in two year public institutions in a recent semester the proportion who earned a bachelor s degree within six years was 0 399 The president of a certain junior college believes that the proportion of students who enroll in her institution have a higher completion rate a State the null and alternative hypotheses in words b State the null and alternative hypotheses symbolically c Explain what it would mean to make a Type I error d Explain what it would mean to make a Type II error a State the null hypothesis in words Choose the correct answer below OA Among students who first enroll in two year public institutions the completion rate is 0 399 OB Among students who enroll at the certain junior college the completion rate is 0 399 OC Among students who enroll at the certain junior college the completion rate is less than 0 399 OD Among students who enroll at the certain junior college the completion rate is greater than 0 399

the consequences of making a Type I error are severe would you choose the level of significance x to equal 0 01 0 05 or 0 10 Choose the correct answer below OA 0 01 OB 0 05 0 10

State the conclusion based on the results of the test According to the Federal Housing Finance Board the mean price of a single family home two years ago was 299 700 A real estate broker believes that because of the recent credit crunch the mean price has decreased since then The null hypothesis is not rejected Choose the correct answer below OA There is not sufficient evidence to conclude that the mean price of a single family home has increased from its level two years ago of 299 700 OB There is sufficient evidence to conclude that the mean price of a single family home has decreased from its level two years ago of 299 700 OC There is sufficient evidence to conclude that the mean price of a single family home has increased from its level two years ago of 299 700 OD There is not sufficient evidence to conclude that the mean price of a single family home has decreased from its level two years ago of 299 700

Select the correct choice that completes the sentence below This is a reading assessment question Be certain of your answer because you only get one attempt on this question The hypothesis denoted H is a statement that the researcher is trying to find evidence to support

The null and alternative hypotheses are given Determine whether the hypothesis test is left tailed right tailec or two tailed What parameter is being tested Ho 120 H 120 Is the hypothesis test left tailed right tailed or two tailed OTwo tailed test O Right tailed test O Left tailed test What parameter is being tested Population mean O Population standard deviation Population proportion

10 Find the standard deviation of the sample data set 6 82 8 68 5 20 7 02 7 63 9 32 4 28 9 28 5 31 Round your answer to the nearest hundredths Answer

7 pts We want to estimate with 95 confidence the average daily sales by various box stores during the holiday season We take a random sample of 45 box stores in the northwest region and find that on average x 10 254 in sales per day with a standard deviation of sx 1 181 per day a Do we meet the conditions for the CLT Explain why Yes we meet the conditions for the CLT because the sample size is sufficiently large n 45 and the population standard deviation is known This allows us to assume that the sampling distribution of the sample mean is approximately normally distributed regardless of the distribution of the population b What are the degrees of freedom of our t distribution and what is our T score for this confidence interval No work to be shown just checking a calculation n 1 45 1 44 T score 2 0154 C ta form below Write out your confidence interval in x ta

1 A university wants to claim that more than 80 of its students find a full time job within 1 year of graduating What symbol below is the appropriate symbol to use in the null and alternative hypothesis OF Ox Op Op Continue Reset answer

3 8 pts The amount of time students spend on a statistics assignment has a standard deviation of o 11 minutes If we take a random sample of 36 students and they average 42 minutes on their assignment construct and interpret a 95 confidence interval estimating the true population average amount of time it takes to complete the assignment a What is the sample statistic x Sample statistic 42 minutes b Do we meet conditions of the Central Limit Theorem to be able to construct this confidence interval Explain why Yes we meet the conditions for the CLT because the sample size iis sufficiently large n 4 and both the random sample and population deviation is known This allows us to assume hat the sampling distribution of the sample mean is approximately normally distributed egardless of the distribution of the population c Write the confidence interval in the form x Za So I can see the values pieces of our formula written explicitly 42 1 96 6 38 40666667 45 59333333

2 A manufacturer consistently ships 100 units each week to clients and wants to claim that the average number of defective product in all shipments is less than 2 4 What symbol below is the appropriate symbol to use in the null and alternative hypothesis O Op Ox Op

8 pts We want to estimate the proportion of University of Montana Missoula College students who support a new bill regarding minimum wage We collect a simple random sample from 200 students and 109 say they support the new bill Construct a 95 confidence interval estimating the proportion of UM MC students who support the bill a What is our sample statistic p Sample statistic 0 549 54 5 b Do we meet normality conditions AKA the conditions of the Central Limit Theorem for proportions Justify your response 0 545 109 200 np n p 200 1 0 545 91 Since both the np and n 1 p are greater than 10 we do meet the normality conditions c What is the margin of error for this confidence interval Explicitly show the pieces of your calculation so I can check for errors

8 pts The amount of time students spend on a statistics assignment has a standard deviation of o 11 minutes If we take a random sample of 36 students and they average 42 minutes on their assignment construct and interpret a 95 confidence interval estimating the true population average amount of time it takes to complete the assignment a What is the sample statistic x Sample statistic 42 minutes b Do we meet conditions of the Central Limit Theorem to be able to construct this confidence interval Explain why

If we are given a 95 confidence interval estimating the proportion of patients at a hospital who have previously had covid as 0 630 0 758 what was the sample size used to create this confidence interval Hint Write out the formula for the confidence interval what is p what other values do you need to solve to find n

75 seconds 1 minute 60 seconds 1 25 Therefore the margin of error in minutes is E 1 25 Confidence Level Step 2 A sample size for 95 confidence is needed Common values for z for various confidence levels are given below a 2 90 95 99 1 25 minutes a a 2 Submit Skip you cannot come back 0 10 0 05 1 645 0 05 0 025 0 01 0 005 za 2 1 960 1 25 minutes 2 576 Za 2 According to the table for a 95 confidence interval the necessary value for is

You may need to use the appropriate appendix table or technology to answer this question Consider a binomial experiment with n 20 and p 0 70 Round your answers to four decimal places a Compute f 12 f 12 b Compute f 16 f 16 c Compute P x 16 P x 16 d Compute P x 15 P x 15 e Compute E x E x f Compute Var x and a Var x a

You may need to use the appropriate appendix table or technology to answer this question Market share analysis company Net Applications monitors and reports on internet browser usage According to Net Applications in the summer of 2014 Google s Chrome browser exceeded a 20 market share for the first time with a 20 37 share of the browser market For a randomly selected group of 25 Internet browser users answer the following questions Round your answers to decimal places a Compute the probability that exactly 9 of the 25 Internet browser users use Chrome as their Internet browser Round your answer to four decimal places b Compute the probability that at least 3 of the 25 Internet browser users use Chrome as their Internet browser Round your answer to four decimal places c For the sample of 25 Internet browser users compute the expected number of Chrome users d For the sample of 25 Internet browser users compute the variance and standard deviation for the number of Chrome users Round your answers to four decimal places variance standard deviation

o MY NOTES According to a 2017 Wired magazine article 40 of emails that are received are tracked using software that can tell the email sender when where and on what type of device the email w Wired magazine website Suppose we randomly select 40 received emails a What is the expected number of these emails that are tracked b What are the variance and standard deviation for the number of these emails that are tracked Round your answers to three decimal places Var x Need Help ASK YOUR TEACHER Read It PRACTICE A

Here is a sample data set 17 8 45 16 28 50 46 13 0 a Find the smallest number Minimum from the data set b Find the first quartile Q1 c Find the median d Find the third quartile Q3 e Find the largest number Maximum from the data set

Run a regression analysis on the following bivariate set of data with y as the response variable X y 60 9 27 7 88 4 140 1 56 4 17 8 78 6 91 5 55 5 47 8 69 6 55 4 77 8 91 5 93 1 83 2 56 7 44 5 76 7 92 2 64 7 79 64 4 7 2 Find the correlation coefficient and report it accurate to three decimal places r What proportion of the variation in y can be explained by the variation in the values of x Report answer as a percentage accurate to one decimal place If the answer is 0 84471 then it would be 84 5 you would enter 84 5 without the percent symbol r Based on the data calculate the regression line each value to three decimal places Predict what value on average for the response variable will be obtained from a value of 80 9 as the explanatory variable X What is the predicted response value Report answer accurate to one decimal place

5 10 15 data 20 25 I to 30 Based on the boxplot above identify the 5 number summary 0 0 0 0 0

Below is a sample data set 20 11 36 33 26 Find the median 42 5

You may need to use the appropriate appendix table or technology to answer this question For a two tailed hypothesis test with a sample size of 38 and a 0 10 level of significance what are the critical values of the test statistic t O 1 687 and 1 687 O 1 686 and 1 686 1 305 and 1 305 O 1 304 and 1 304 Need Help Submit Answer Read It

You may need to use the appropriate appendix table or technology to answer this question Consider the following hypothesis test Ho 17 H 17 A sample of 81 provides a sample mean of 16 and a sample standard deviation of 4 a Determine the standard error of the mean Round your answer to five decimal places b Compute the value of the test statistic Round your answer to three decimal places c Determine the p value and using a 0 05 test the above hypotheses Find the p value Round your answer to four decimal places p value State your conclusion O Do not reject Ho There is sufficient evidence to conclude is less than 17 Reject Ho There is sufficient evidence to conclude is less than 17 Do not reject Ho There is insufficient evidence to conclude is less than 17 Reject Ho There is insufficient evidence to conclude is less than 17

p Confidence Level 90 95 100 99 given percentage 100 a a 2 According to the table for a 95 confidence level we have Za 2 1 96 0 10 0 05 za 2 Step 2 At one point it was estimated that 26 of stay at home parents were fathers Since this is the only known estimate it will be used to find the planning value for the population p 1 645 0 05 0 025 1 960 0 01 0 005 2 576 1 960

You may need to use the appropriate appendix table or technology to answer this question Sixty eight percent of online courses taught at community colleges nationwide were taught by full time faculty To test if 68 also represents California s percent for full time faculty teaching the online classes Long Beach City College LBCC in California was randomly selected for comparison In the same year 34 of the 44 online courses LBCC offered were taught by full time faculty Conduct a hypothesis test at the 5 level to determine if 68 represents California State the null and alternative hypotheses Enter for as needed Ho 0 68 H 0 68 X X What is the test statistic Round your answer to two decimal places 1 3182 What is are the critical value s If using the z distribution round your answer s to two decimal places and if using the t distribution round your answer s to three decimal places Enter NONE for any unused answer blanks lower tail upper tail X X What is the decision of the test and what conclusions can be drawn O At the 5 level of significance we would reject Ho and conclude that there is sufficient evidence to conclude that the percent of online courses taught at community colleges in the state is not equal to 68 O At the 5 level of significance we would fail to reject Ho and conclude that there is sufficient evidence to conclude that the percent of online courses taught at community colleges in the state is not equal to 68 O At the 5 level of significance we would fail to reject Ho and conclude that there is not sufficient evidence to conclude that the percent of online courses taught at community colleges in the state is not equal to 68 O At the 5 level of significance we would reject Ho and conclude that there is not sufficient evidence to conclude that the percent of online courses taught at community colleges in the state is not equal to 68

In the past 26 of all homes with a stay at home parent had the father as the stay at home parent An independent research firm has been charged with conducting a sample survey to obtain more current information a What sample size is needed if the research firm s goal is to estimate the current proportion of homes with a stay at home parent in which the father is the stay at home parent with a margin of error of 0 05 Use a 95 confidence level b Repeat part a using a 99 confidence level Step 1 a What sample size is needed if the research firm s goal is to estimate the current proportion of homes with a stay at home parent in which the father is the stay at home parent with a margin of error of 0 05 Use a 95 confidence level To get the sample size necessary to obtain a particular margin of error the following formula will be used where Z 2 is the z value corresponding to an upper tail area of and a confidence level of 1 a p is the planning value for the point estimate of the population proportion and E is the desired margin of error 2 za 2 p 1 p E The desired margin of error is 0 05 for a 95 confidence level This confidence level will be used to determine the value of Z 2 Common values for 2 2 for various confidence levels are given below n Confidence Level 90 95 99 R 0 10 a 2 0 05 1 645 0 05 0 025 Za 2 0 01 0 005 1 960 2 576 to the table for a 95 confidence level we have Za 2

Are all batteries created equal An experiment was carried out to determine this Two brand name battery companies and a generic company were compared D batteries were put into flashlights and continuously left on The data provided is the number hours the flashlight remained lit Is this sufficient evidence to determine if the mean times for the different companies are different Use a 0 05 significance level What are the hypothesis statements for this situation H 2 G HA at least one mean is different Ho P1 P2 PG HA at least one proportion is different Ho Battery type and time are independent HA Battery type and time are dependent

b The desired margin of error is 0 06 CHER You may need to use the appropriate appendix table or technology to answer this question The U S Energy Information Administration US EIA reported that the average price for a gallon of regular gasoline is 2 94 The US EIA updates its estimates of average gas prices on a weekly ba Assume the standard deviation is 0 25 for the price of a gallon of regular gasoline and recommend the appropriate sample size for the US EIA to use if they wish to report each of the following margins of error at 95 confidence Round your answers up to the nearest whole number a The desired margin of error is 0 10 c The desired margin of error is 0 04 PRACTICE ANOTHER