Statistics Questions

The mean SAT score in mathematics is 508 The standard deviation of these scores is 31 A special preparation course claims that the mean SAT score u of its graduates is greater than 508 An independent researcher tests this by taking a random sample of 37 students who completed the course the mean SAT score in mathematics for the sample was 518 Assume that the population is normally distributed At the 0 05 level of significance can we conclude that the population mean SAT score for graduates of the course is greater than 508 Assume that the population standard deviation of the scores of course graduates is also 31 Perform a one tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places and round your responses as specified below If necessary consult a list of formulas a state the null hypothesis Ho and the alternative hypothesis H H 0 b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places d Find the p value Round to three or more decimal places H x X a S OSO D P Q 00 NO DO

Last year s mean hourly wage in dollars for all hospital clerical workers in a large state was 6 75 An administrator for the state believes that this year s mean hourly wage for hospital clerical workers is greater than last year s mean She hires statisticians to sample a number of hospital clerical workers and to carry out a hypothesis test State the null hypothesis Ho and the alternative hypothesis H that would be used for this test H 0 o 0 X D P S

Commute times to a major city follows the normal probability distribution and the standard deviation is 4 5 minutes Arandon Sample of 104 Commute times is given below in minutes Use Excel to find the 98 confidence interval for he mean travel time in minutes Round your answers to one decimal place and use ascending order Time 4 6 2 3 5 8 0 15 35 40 40 34 32 35 31 15 4 1 37 40 31 14 39 14 11 33 38 21 35 33 34 27 31 26 35 32 18 40 17 32 38 28 21 33 12 24 23 24 37 30 28 10 13 33 0 0 8 5 20 lo 41 36 13 38 39 37 33 39 41 17 113 40 128 dy I F F 12 35 16 34 29 36 32 20121 27 1 34 32 2511 16 21 34 13 C 29 ar 23 34 R 33 37 39 36 11 42 33

Alison the owner of a regional chain of pizza stores is trying to decide whether to add calzones to the menu She conducts a survey of 700 people in the region and asks whether they would order calzones if they were on the menu 46 people responded yes Create a 90 confidence interval for the proportion of people in the region who would order calzones if they were on the menu Round your answer to four decimal places Provide your answer below

In a survey of 329 people who attended a local professional soccer team s most recent home game 141 said that they were fans of the visiting team Create a 95 confidence interval for the population proportion of attendees who were fans of the visiting team Use Excel to create the confidence interval rounding to four decimal places Provide your answer below

There are 7 acts in a talent show A dancer a juggler a magician a pianist a singer a violinist and a whistler A talent show host randomly schedules the 7 acts Compute the probability of each of the following events Event A The first four acts are the whistler the juggler the pianist and the magician in any order Event B The singer is first the juggler is second the magician is third and the pianist is fourth Write your answers as fractions in simplest form P A P B 00

1 ile shop manager timed ar employees and recorded the time in minutes it took them to chang a water pump Assuming normality Use Excel to find the 99 confidence interval for the true mean Round your answers to three decimal places and use Increasing order Time 18 4 1601 19 5 16 5 12 5 13 8 17 9 9 8 23 8 18 7 15 0 19 2 17 0 11 5 15 7 22 5 23 7 15 0 17 8 20 7

assessor wants to assess the Mean property tax bill for all homeowners in a certain state From a survey ten years ago a sample of 28 property tax bills is given below Assume the property tax bills are approximately normally distributed use Excel to construct 95 confidence interval for the population mean property tax bill Round your answers to two decimal places and use increasing order wh PEL Property Tax Bill 715 1715 35 1157 82 02651 10 2465 656 1784 28 P 2016 999 00402 99 08 1028 76 1571 23 1093 36 001609 220 1346 65 001391 4701 1574 00 E OPG398 89 91447 78e 1098 81 CICL 2018 33 Tra 2156 75 13 1710 81 539 424 OL1579 48 TL OP 699 56 2222 16

A business magazine conducted a survey of 751 employees who had been at their current employer for 5 or more years Of these employees 295 responded that they were bored in their current position Create a 99 confidence interval for the proportion of employees who have been with their current employer for 5 or more years and reported being bored in their current position Use Excel to create the confidence interval rounding to four decimal places Provide your answer below

majoring V A One Sample 2 test for proportion V B N 29 X 12 V v C1 Ho p 0 25 Test at the 05 Significance level Ho p 0 25 Right tail C 6 2 Critical value 1 65 C 3 Test value 2 04 CC 4 Since the test value is greater than the critical value we reject the hypothesis G5 We have sufficient evidence to Conclude that more than 25 of Class is majoring in nursing at

A psychologist is interested in the mean IQ score of a given group of children It is known that the IQ scores of the group have a standard deviation of 14 The psychologist randomly selects 50 children from this group and finds that their mean IQ score is 106 Based on this sample find a 95 confidence interval for the true mean IQ score for all children of this group Then give its lower limit and upper limit Carry your intermediate computations to at least three decimal places Round your answers to one decimal place If necessary consult a list of formulas Lower limit Upper limit X

Gary is studying the prevalence of regional dialects He surveyed 351 people in a region and asked what words they used for certain things 292 of the respondents referred to soft drinks as pop as opposed to soda or cola Create a 90 confidence interval for the proportion of people in this region who refer to soft drinks as pop Use Excel to create the confidence interval rounding to four decimal places Provide your answer below

Suppose that the lifetimes of old fashioned TV tubes are normally distributed with a standard deviation of 1 2 years Suppose also that exactly 20 of the TV tubes die before 5 years Find the mean lifetime of TV tubes Carry your intermediate computations to at least four decimal places Round your answer to at least one decimal place years X

A restaurant is reviewing customer complaints In a sample of 227 complaints 57 complaints were about the slow speed of the service Create a 95 confidence interval for the proportion of complaints that were about the slow speed of the service Use Excel to create the confidence interval rounding to four decimal places Provide your answer below

IV 21 X 12 lest at the 05 Signific level Ho p 0 25 Hoip 0 25

In a random sample of 2 282 college students 356 reported getting 8 or more hours of sleep per night Create a 95 confidence interval for the proportion of college students who get 8 or more hours of sleep per night Use Excel to create the confidence interval rounding to four decimal places Provide your answer below

Suppose Z follows the standard normal distribution Use the calculator provided or this table to determine the value of c so that the following is true P Z c 0 8888 Round your answer to two decimal places

any wants to determine a Confidence interval for the average CPU time of its teleprocessing transactions A sample of 70 random transactions in milliseconds is given below Assume that the transaction times follow a normal distribution with a standard deviation of 600 milliseconds Use Excel to determine a 98 confidera interval for the average CPU time in milliseconds Round your answers to the nearest integer and use Ascending order Time 6690 6160 5140 7210 5570 7320 5190 5770 8390 6730 6820 5340 6690 5560 6680 72 70 5670 6650 6180 5570 5410 6160 6600 6910 6400 4960 5660 6360 5760 6270 6810 5860 5700 6730 4850 6160 6490 6790 6680 6160 5500 5490 5240 7020 5930 6380 5140 6270 6200 5770 5480 6090 6040 6380 4910 4170 6630 5990 4720 6570 5860 6610 5370 6510 5800 5660 5760 6110

owing data represent a random sample for the ages of 41 players in a basebal league Assume that the population is normally distributed with a standard deviation of 2 1 years Use Excel to find the 98 confidere interval for the true mean age of players in this league Round your answers to three decimal places and use ascending order Age 29 31 30 23 24 30 24 F G H I J 8 30 34 30 28 28 31 25 25 De 34 32 30 24 31 32 36 32 25 25 98 27 25 33 29 32 C 20

Click the following link to view Saving and Investment data from FRED Then use that data to answer the following questions Real time data provided by Federal Reserve Economic Data FRED Federal Reserve Bank of Saint Louis For this exercise you will need to enter data from FRED for real gross private domestic investment GPDIC1 real private nonresidential fixed investment PNFIC1 and re private residential fixed investment PRFIC1 Using the data from FRED enter the values for the second quarter of 2023 shown as 2023 04 01 on FRED for the following series IDs Enter your answers exactly a they appear on FRED Title Real Gross Private Domestic Investment Real Private Nonresidential Fixed Investment Real Private Residential Fixed Investment Series ID GPDIC1 PNFIC1 PRFICI Value billions of constant dollars

A dartboard has 5 equally sized slices numbered from 1 to 5 Some are grey and some are white The slices numbered 3 and 4 are grey The slices numbered 1 2 and 5 are white A dart is tossed and lands on a slice at random Let X be the event that the dart lands on a grey slice and let P X be the probability of X Let not be the event that the dart lands on a slice that is not grey and let P not X be the probability of not X Event 1 0 Outcomes a For each event in the table check the outcome s that are contained in the event Then in the last column enter the probability of the event 2 3 4 5 Probability P X 00 4 X 5 3 1 2

is majoring in nursing What type of hypothese Should I use A Example Ho p 0 25 Hai p 70 25 or B Ho p 0 25 H p L 0 23 C Ho p 0 25

Claim more than 25 of our Class is majoring in nursing N 29 X 17 Ho p 0 25 Ha p20 25 Test at the 05 Signific level 0

There is some speculation that a simple name change can result in a short term increase in the price of certain business firms stocks relative to the prices of similar stocks Suppose that to test the profitability of name changes we analyze the stock prices of a large sample of corporations shortly after they changed names and we find that the mean relative increase in stock price was about 0 72 with a standard deviation of 0 19 Suppose that this mean and standard deviation apply to the population of all companies that changed names Complete the following statements about the distribution of relative increases in stock price for all companies that changed names a According to Chebyshev s theorem at least Choose one of the relative increases in stock price lie between 0 34 and 1 10 b According to Chebyshev s theorem at least 56 of the relative increases in stock price lie between and Round your answer to 2 decimal places X

2 C Ho Hi t2 0 HA H1 H 0 Compute the t statistic Let the difference of the sample means be y y2 t 7 Round to three decimal places as needed Find the P value The P value is Round to four decimal places as needed State the conclusion Recall that 0 05 Fail to reject Ho There is insufficient evidence to reject the claim that the b Find a 95 confidence interval using the pooled degrees of freedom Data table Neighborhood 1 56 58 59 65 48 44 Print Neighborhood 2 48 37 57 54 40 52 Done U Round to two decimal places as needed c A 95 confidence interval for the mean difference in ages of houses in the two neighborhoods was 3 08 17 08 Is this result different from the resu Fxplain why or why not Choose the correct answer below

In a recent survey 8 college graduates were each asked for the number of hours they work each week Here is a list of the responses 38 39 53 42 53 43 37 44 Find the range of the data set A

Atype of golf ball is tested by dropping it onto a hard Surface from a height I meter The height it bounces is known to be normally distributed A sample of 25 balls is tested and the bounce heights are given below Use Excel to find a 95 confidence interval for the mean bounce height of the golf ball Round answers to two decimal places and use your Increase order Height ET 81 4 82 0 80 8 76 3 84 4 85 6 82 9 76 0 80 0 83 2 8018 79 6 82 9 83 4 86 0 76 2 84 8 77 0 75 4 82 0 79 8 80 4 86 9 82 1 2h 01 2wash 01 0281

2 There are 108 feet in 36 yards What is the constant of proportionality that relates y the number of yards to x the number of feet

Judging on the basis of experience a politician claims that 46 of voters in a certain area have voted for an independent candidate in past elections Suppose you surveyed 25 randomly selected people in that area and 12 of them reported having voted for an independent candidate The null hypothesis is that the overall proportion of voters in the area that have voted for an independent candidate is 46 What value of the test statistic should you report The test statistic is z Round to two decimal places as needed

A random sample of American toads were measured and the proportion of toads that were over 1 ounce in weight recorded The measurements resulted in a sample proportion of p 0 16 with a sampling standard deviation of Op 0 02 Using the empirical rule write a 95 confidence interval for the true proportion of American toads that are over 1 ounce in weight Provide your answer below

In a random sample of 30 young bears the average weight at the age of breeding is 312 pounds Assuming the population ages are normally distributed with a population standard deviation is 30 pounds use the Empirical Rule to construct a 68 confidence interval for the population average of young bears at the age of breeding Do not round intermediate calculations Round only the final answer to the nearest pound Remember to enter the smaller value first then the larger number Provide your answer below

article study include the sample size and the level of confidence used to create the confidence interval Explain what the confidence interval means in context of the news article or scholarly source Follow Up Post Instructions Respond to at least one peer Further the dialogue by providing more information and clarification Here are some suggested responses How do you think the confidence interval that was presented in the study was calculated Explain the mathematical concepts could extract from this article study Writing Requirements O Summ

In a questionnaire a random sample of teachers were asked whether they provide extra credit to students in their class The questionnaire resulted in a sample proportion of p 0 27 with a sampling standard deviation of op 0 03 who mentioned they provide extra credit Using the empirical rule write a 99 7 confidence interval for the true proportion of teachers who provide extra credit Provide your answer below

A random sample of residents of a city were asked whether they were satisfied with the city s public transportation system The survey resulted in a sample proportion of p 0 4 with a sampling standard deviation of op 0 07 Using the empirical rule write a 95 confidence interval for the true proportion of satisfied residents Round answers to two decimal places Provide your answer below

A technician randomly sampled repair logs for computers at a university He wanted to find out how many times the computers were repaired The proportion of computers that were repaired more than three times in the last two years was 0 24 with a margin of error of 0 03 Construct a confidence interval for the proportion of university computers that were repaired more than three times in the last two years Provide your answer below

A researcher is trying to estimate the population mean for a certain set of data The sample mean is 45 and the error bound for the mean is 9 at a 99 7 confidence level So 45 and EBM 9 Find and interpret the confidence interval estimate Select the correct answer below O We can estimate with 99 7 confidence that the true value of the population mean is between 42 and 48 O We can estimate with 99 7 confidence that the true value of the population mean is between 36 and 54 O We can estimate with 99 7 confidence that the true value of the population mean is between 45 and 54 We can estimate with 99 7 confidence that the true value of the population mean is between 36 and 54 O We can estimate with 99 7 confidence that the true value of the population mean is between 39 and 51 We can estimate with 99 7 confidence that the true value of the population mean is between 36 and 45

Claim More than 25 of our class is majoring in nursing or nursing BSN Test at the 05 significance level nstructions Complete a full hypotheses test answering all of the questions here You can use the traditional or p value met Make a copy of this sheet before you begin FileMake A Copy You can use your T184 or online calculator Round all values to 3 decimal places if needed A What type of test will you be running B What is the sample size n for Major 29

Randomly sampled math majors at a large university were asked to take part in a survey about the curriculum The dean wanted to find out how challenging the math coursework was for students The proportion of math majors that stated the curriculum was challenging was 0 92 with a margin of error of 0 07 Construct a confidence interval for the proportion of math majors that stated the curriculum was challenging Provide your answer below

A random sample of school board members in a particular school district were asked about snow days in an upcoming vote The proportion of school board members who planned to vote No on making school days longer to make up for snow days is 0 59 with a margin of error of 0 03 Construct a confidence interval for the proportion of school board members that plan to vote No on the issue Provide your answer below

Height 43in 62 in 83in 62 in Shoe 6 9 9 5 10 2 1 Taking confidence level 90 2 1 0 90 0 1 2 sample m mee 65 in 10 G SAI 563 l62 56 n CI 7 b Sample mean Sample storelard deviation Sx 1 xi x n 1 11 62 Ty Eyi 85 5 19 5 9 Sy 1 Elyi F 11 73 68 in 68 in 48 in 64in 12 8 10 c 90 confidence intenol x T df x s df 9 1 8 1 2 0 95 df 8 To 95 8 1 86 v CI 62 56 1 86 11 62 vy d 90 CI for shoe size of population y In T x df x To 9 181 1 86 9 5 1 86 x 1 73 9 5 1 07 19 55 36 69 78 4 CLO 3 Find a correlation between height and shoe size a Create a scatterplot of the data Height is x axis and Shoe size is y axis Attach your scatterplot to the end of this document b Find the linear correlation coefficient What does this tell you about your data c Write the equation of the regression line and use it to predict the shoe size of a person that is 68 inches tall 5 Write a paragraph or two about what you have learned from this process When you read see or hear a statistic in the future what skills will you apply to know whether you can trust the result

Shown below are the scatter plots for four different data sets Answer the questions that follow The same response may be the correct answer for more than one question 3 4 5 6 7 8 9 10 11 Figure 1 9 8 0 2 3 4 5 6 7 8 9 10 11 Figure 2 1 For which data set is the correlation coefficient r closest to 1 2 Which data set indicates the strongest negative linear relationship between its two variables 3 For which data set is the correlation coefficient r closest to 0 X x x 4 5 6 7 8 9 10 11 Figure 3 Choose one Choose one X Choose one 10 8 X X X X 23456 7 8 9 10 11 Figure 4

Do bonds reduce the overall risk of an investment portfolio Let x be a random variable representing annual percent return for the Vanguard Total Stock Index all Stocks Let y be a random variable representing annual return for the Vanguard Balanced Index 60 stock and 40 bond For the past several years assume the following data Compute X A O 12 0 6 4879 O 5311 05033 4 39 27 24 15 33 26 27 12 25 17 15 4 12 5 24 6

K A genetic experiment involving peas yielded one sample of offspring consisting of 428 green peas and 145 yellow pea eas same circumstances 27 of offspring peas will be yellow Identify the null hypothesis alternative hypothesis test statistic P value conclusion about the null hypothesis and final conclusion addresses the original claim Use the P value method and the normal distribution as an approximation to the binomial distribution What are the null and alternative hypotheses OA Ho p 0 27 H p 0 27 OC Ho p 0 27 H p 0 27 E Ho p 0 27 H p 0 27 What is the test statistic Z 0 91 Round to two decimal places as needed What is the P value P value Round to four decimal places as needed OB Ho p0 27 H p 0 27 O D Ho p 0 27 H p 0 27 OF Ho p 0 27 H p 0 27

the claim that lew than half of Americans prefer to watch the news rather than read or listen to it Use the P value method Use the normal distribution as an approximation to the binomial distribution Let p denote the population proportion of all Americans who prefer to watch the news rather than read or listen to it Identify the null and alternative hypotheses Ho P 0 5 H p 0 5 Type integers or decimals Do not round Identify the test statistic Z 1 69 Round to two decimal places as needed Identify the P value P value 0 Round to three decimal places as needed

K Listed below are the lead concentrations in g g measured in different Ayurveda medicines Ayurveda is a traditional medical system commonly used in India The lead concentrations listed here are from medicines manufactured in the United States Assume that a simple random sample has been selected Use a 0 10 significance level to test the claim that the mean lead concentration for all such medicines is less than 14 0 g g 3 02 6 54 5 96 5 54 20 54 Identify the null and alternative hypotheses HoH 14 H H 14 Type integers or decimals Do not round Identify the test statistic Round to two decimal places as needed 7 50 12 02 20 51 11 49 17 53 5

K In a study of cell phone usage and brain hemispheric dominance an Internet survey was e mailed to 6969 subjects randomly selected from an online group involved with ears There were 1320 surveys returned Use a 0 01 significance level to test the claim that the return rate is less than 20 Use the P value method and use the normal distribution as an approximation to the binomial distribution Identify the null hypothesis and alternative hypothesis A Ho p 0 2 H p 0 2 OC Ho p 0 2 H p 0 2 OE Ho p 0 2 H p 0 2 The test statistic is z 0 Round to two decimal places as needed OB Ho p 0 2 H p 0 2 OD Ho p0 2 H p 0 2 OF Ho p 0 2 H p 0 2

Listed below are the lead concentrations in g g measured in different Ayurveda medicines Ayurveda is a traditional medical system commonly used in India The lead concentrations listed here are from medicines manufactured in the United States Assume that a simple random sample has been selected Use a 0 10 significance level to test the claim that the mean lead concentration for all such medicines is less than 14 0 g g 3 02 6 54 5 96 5 54 20 54 Identify the null and alternative hypotheses Ho H Type integers or decimals Do not round 7 50 12 02 20 51 11 49 17 53

A poll of 1052 Americans showed that 47 4 of the respondents prefer to watch the news rather than read or listen to it Use those results with a 0 01 significance level to test the claim that fe than half of Americans prefer to watch the news rather than read or listen to it Use the P value method Use the normal distribution as an approximation to the binomial distribution Let p denote the population proportion of all Americans who prefer to watch the news rather than read or listen to it Identify the null and alternative hypotheses Ho P H P Type integers or decimals Do not round

2 1 Taking candince level 90 1 0 90 10ll 2 sample mesa x xi 562 62 56 Sample standard deviation Sx 1 xi x n l 11 62 y Eyt 85 5 Sy 1 Elyi y 1 73 h 1 b Sample mean c 90 confidence intenol x T df x 5 df 9 1 8 1 0 95 df 8 VF To 95 8 1 86 T55 36 69 767 85 5 19 5 CI 62 56 1 86 x 11 62 vy y To 9 181 1 86 d 90 CI for shoe size of population T df x in 25 1 26 1 73 9 5 1 07 4 st Coast University Signature Assignment Page 2 of 2 CLO 2 Test a claim that the mean height of your population is different from 64 inches Use the appropriat significance level a you fixed earlier a State the initial and alternative hypothesis b Find the test statistic and the P value You can use StatCrunch Microsoft Excel or any other statistical tool to write the statistic and then substitute your appropriate numbers c Draw a conclusion in context of the situation Your conclusion should include both the formal language as well as an informal explanation CLO 3 Find a correlation between height and shoe size a Create a scatterplot of the data Height is x axis and Shoe size is v axis Attach your scatterplot to the end

people I used are my cousing family ousin s wedding I went around and asked a couple people membere ight in inches and their shoe size I think my an accurate representation because they re different sizes Person 2 poson 3 Person 62 in 83 in 62 in 9 9 5 10 Perse 65 in 10 person 6 person besson person person 9 68 in 68 in 48 in 64 in 71 8 10 12 2 CLO 1 Construct a confidence interval to estimate the mean height and the mean shoe size you must complete the following questions by first choosing a Confidence Level You may choose from the familiar 90 95 or 99 level of confidence Denote this by choosing a a Find the sample mean and sample standard deviation of the height Denote them as x and sx respectively b Find the sample mean and sample standard deviation of the shoe sizes Denote them as y and sy respectively I c Construct and interpret a confidence interval to estimate the mean height of the population You can use StatCrunch Microsoft Excel or any other statistical tool for the confidence interval and then substitute your appropriate numbers d Construct and interpret a confidence interval to estimate the mean shoe size of the population You can use StatCrunch Microsoft Excel or any other statistical tool for the confidence interval and then substitute your appropriate numbers