Statistics Questions

Use the data values in the table below to calculate the correlation between the variables x and y X y 8 05 9 8 25 9 1 8 65 5 6 7 8 9 10 9 Give your answer to three decimal places

Independent random samples of managers yearly salaries in 1 000 taken from governmental and private organizations provided the following information Test to determine if there is a sig difference between the average salaries of the managers in the two sectors O O O 1 O S n Government Private 79 10 29 a Give the hypotheses for the above Ho HG Hp 20 Ha HG Hp 0 Ho HG Hp 0 H HG Hp 20 Ho HG Hp 0 Ha HG Hp 0 Ho HG Hp 0 Ha HG Hp 0 73 Ho MG Hp 0 Ha HG Hp 0 12 32 b Determine the degrees of freedom Round your answer down to the nearest integer c Compute the test statistic Use Government Private Round your answer to three decimal places d At a 0 05 level of significance test to determine if there is a significant O We do not reject Ho There is no significant difference fference between the average salaries of the managers in the two sectors

5 The following ordered pairs t 1 represent the Olympic year I and 400 meter freestyle swimming event 1952 5 20 1956 4 91 1960 4 84 1964 4 72 1968 4 53 1972 4 32 1976 4 16 1980 4 15 1984 4 12 1988 4 06 1992 4 12 1996 4 12 2000 4 10 2004 4 09 2008 4 05 2020 3 57 a Find an appropriate regression model with t 0 corresponding to 1950 b What is the average rate of change from 1952 to 2020 How does this compare to the rate of change of your regression model 3 When a football is punted it goes up into the air reaches a maximum altitude then comes back down When the ball was kicked it was 4 feet above the ground One second later it was 28 feet above the ground Two seconds after it was kicked the football was 20 feet up a Define the variables Independent x b Make a table of values and sketch a graph with appropriate labels c Find the quadratic equation y d Find the coordinates of the vertex Explain its meaning Dependent y e For how long is the football above 20 feet

Based on the data shown below calculate the correlation coefficient to three decimal places X y 32 2 35 4 35 2 38 8 4 5 6 7 8 41 9 51 2 10 47 6 11 57 6

Tutorial Exercise Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and pre preview ads before the movie starts Many complain that the time devoted to previews is too long t A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was 5 minutes Use that as a planning value for the standard deviation in answering the following questions a If we want to estimate the population mean time for previews at movie theaters with a margin of error of 75 seconds what sample size should be used Assume 95 confidence b If we want to estimate the population mean time for previews at movie theaters with a margin of error of 1 minute what sample size should be used Assume 95 confidence Step 1 a If we want to estimate the population mean time for previews at movie theaters with a margin of error of 75 seconds what sample size should be used Assume 95 confidence Recall the formula to find a sample size n for a desired margin of error E with a population standard deviation o and 2 2 relates to the level of confidence za 2 E n The sample standard deviation of 5 minutes will be used in place of the population standard deviation However note that the desired margin of error was given to be 75 seconds The standard deviation and margin of error must be in terms of the same units Convert 75 seconds to minutes 1 minute 60 seconds 75 seconds minutes Therefore the margin of error in minutes is E minutes

Step 9 is not sufficient evidence to conclude that the population proportion is less than 0 85 p 0 85 c p 0 80 Recall the previously determined values po 0 85 and n 160 Now we are to find the test statistic for a new sample proportion p 0 80 Use these values to find the test statistic rounding the result to two decimal places Z P Po Po 1 PO n 0 80 0 85 0 85 10 85 160 Enter a number Submit Skip you cannot come back

Which of the following pairs of variables is likely to have a negative correlation Check all that apply The speed of a car and the time to its destination A person s height and their favorite color The number of miles run and the number of calories burned The square footage of a home and its price Years of education and salary

The scatter plot shows the relationship between the number of minutes studying for a test x and the number of mistakes made y The graph shows the scatterplot of the data and a fitted line 174 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 10 10 20 30 10 50 60 70 80 90 100 110 12 Select True or False for each statement based on the scatter plot True False There is a negative association between the amount of time studying for a test and the number of mistakes made Students who studied for a longer period of time tended to make more mistakes There is a linear association between time studying and number of mistakes True False O True False O True False O

As Swiss cheese matures a variety of chemical processes take place The taste of matured cheese is related to the concentration of several chemicals in the final product In a study of cheese in a certain region of Switzerland samples of cheese were analyzed for lactic acid concentration and were subjected to taste tests The numerical taste scores were obtained by combining the scores from several tasters A scatterplot of the observed data is shown below Taste rating 60 0 50 0 40 0 30 0 20 0 10 0 0 0 0 80 1 00 1 20 1 40 1 60 180 2 00 2 20 Lactic acid What is a plausible value for the correlation between lactic acid concentration and taste rating O 0 999 O 0 7 O 0 07 O 0 7

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 Click here to open this data in StatCrunch p value do not round A What is your decision Retain Ho and Reject Ho

You may need to use the appropriate appendix table or technology to answer this question A random sample of 97 tourists in Chattanooga showed that they spent an average of 2 830 in a week with a standard deviation of 123 A sample of 73 tourists in Orlando showed that they spent an average of 2 890 in a week with a standard deviation of 135 We are interested in determining if there is any significant difference between the average expenditures of all the tourists who visited the two cities a Determine the degrees of freedom for this test Round your answer down to the nearest integer 167 X 147 b Compute the test statistic Use Chattanooga Orlando Round your answer to three decimal places c Compute the p value Round your answer to five decimal places d What is your conclusion Let a 0 02 O Reject Ho We can conclude that there is a significant difference between the average expenditures of tourists who visit Chattanooga and Orlando O Do not reject Ho We cannot conclude that there is a significant difference between the average expenditures of tourists who visit Chattanooga and Orlando Reject Ho We cannot conclude that there is a significant difference between the average expenditures of tourists who visit Chattanooga and Orlando O Do not reject Ho We can conclude that there is a significant difference between the average expenditures of tourists who visit Chattanooga and Orlando

Match each scatterplot shown below with one of the four specified correlations 9 O 8 9 Q OQ a 0 29 b 0 90 c 0 97 d 0 25

each scatterplot shown below with one of the four specified correlations 00 O sg 8 5 0 80 oo 00 8 oo 080 80 80 08 0 Q Q a 0 99 b 0 70 c 0 13 d 0 16

If there is strong correlation between two variables it is definitely true that one is causing the other O False True

Here are the scatter plots for two sets of bivariate data with the same response variable The first compares the variables x y The second compares the variables w y O 8 O Questi O O O O 80 Q Which explanatory variable has a stronger relationship with the response variable y O The first variable x has a stronger relationship with the response variable y O The second variable w has a stronger relationship with the response variable y

A correlation of r 85 is found between weekly sales of firewood and cough drops over a 1 year period Which of the following is true O a There is a pretty strong positive linear relationship between sales of firewood and cough drops O b Fire must be the cause of coughing c Temperature is a possible lurking variable that is behind this relationship O d Both a and c are true O e None of the above

What italicized letter represents correlation Ot Or Oz Os O

Negative linear relationships are represented by values of the correlation r that are O greater than zero O less than zero O zero

10 15 NPV calculation Calculate the NPV given the following free cash flows if the appropriate required rate of return is 10 percent YEAR 0 1 2 4 56 CASH FLOWS 70 000 30 000 30 000 30 000 30 000 30 000 30 000

You may need to use the appropriate appendix table or technology to answer this question 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 information reported below carry out a test of this statement Let a 0 05 Ho sample size 400 H women men 167 State the null and alternative hypotheses Enter for as needed 233 Find the value of the test statistic 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 S test statistic 2 State your conclusion O 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 f women in the union is significantly different from one half

Is the average time we shower the same Two hundred and fifty randomly selected citizens from Brazil United States and Germany were asked to report the length of time minutes they spend in the shower Use a 0 10 significance level and the StatCrunch output to determine if the mean time for a shower is the same for these three countries Options Analysis of Variance results Data stored in separate columns Column statistics Column n Mean Std Dev Std Error U S 250 9 84948 1 228919 0 077723662 German 250 9 58676 1 2828753 0 081136157 Brazil 250 10 03888 1 2476891 0 078910787 ANOVA table Source DF Columns Error 747 1173 472 1 570913 Total 749 1199 2475 In the space 20 x SS MS F Stat P value 2 25 775554 12 887777 8 2040045 0 0003

In October 2021 Pew Research surveyed 9 676 Americans and how they see the availability of affordable housing in their local community Here are the results below Men Women Total A major A minor problem problem Total 2 082 1 893 757 4 732 2 571 1 681 692 4 944 4 653 3574 1 449 9 676 Use a 0 05 significance level to determine if the respondent s sex is independent of their opinion Click here to open the contingency table in StatCrunch Ho Sex and housing opinion are Not a problem A P value type it exaotlu HA Sex and housing opinion are N

Independent random samples of managers yearly salaries in 1 000 taken from governmental and private organizations provided the following information Test to determine if there is a significant difference between the average salaries of the managers in the two sectors O X S O n Government 79 10 29 Ho HG Hp 0 Ha HG Hp 20 a Give the hypotheses for the above Ho HG Hp 20 H HG Hp 0 Ho HG Hp 0 Ha HG Hp 0 Private Ho HG Hp 0 H HG Hp 0 73 12 32 Ho HG Hp 0 H HG Hp 0 b Determine the degrees of freedom Round your answer down to the nearest integer c Compute the test statistic Use Government Private Round your answer to three decimal places d At a 0 05 level of significance test to determine if there is a significant difference between the average salaries of the managers in the two sectors O We do not reject Ho There is no significant difference We do not reject Ho There is a significant difference

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 Ho 1 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

Which summary statement best reflects the findings of the hypothesis test above The sample data suggests that the mean lifetime of the batteries for the the 3 types are not different The sample data suggests that the mean lifetime of the batteries for the the 3 types are different The sample data suggests that the proportion of batteries is the same for all three types The sample data suggests that battery life and battery type are dependent

A Tax Prep Time hrs 7 B 0 1 2 33 34 35 36 37 38 618949 39 40 35 3 30 5 37 4 26 5 13 49 9 28 8 44 61 6 0 5 40 5 34 9 47 9 36 6 24 1 39 8 47 8 18 5 36 6 39 2 14 5 37 3 40 5 49 3 45 5 28 3 19 5 5 6 52 6 41 4 45 3 39 33 7 29 4 14 5 40 1 33 7 36 9 5 6 33 7 B Interval Estimate of a Population Mean Sigma Known Case Sample Size Sample Mean Population Standard Deviation Confidence Coefficient Level of Significance Margin of Error Point Estimate C I Lower Limit C I Upper Limit Data range A A 10 0 95 E F Formulas Used N A N A N A N A N A N A N A G

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 a To get the sample size necessary to obtain a particular margin of error the following formula will be used where Za 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 given below a 2 n Confidence Level 90 95 99 a a 2 za 2 0 10 0 05 1 645 0 05 0 025 1 960 0 01 0 005 2 576 According to the table for a 95 confidence level we have za 2 Common values for Za 2 for various confidence levels are

You may need to use the appropriate appendix table or technology to answer this question Consider the following hypothesis test H Hi H2 S 0 H Mi M2 0 The following results are for two independent samples taken from two populations Sample Size Sample Mean Sample Variance 78 Sample 1 38 42 142 Sample 2 34 36 171 a Determine the degrees of freedom for the t distribution Use Sample 1 Sample 2 Round your answer down to the nearest integer X b Compute the test statistic Round your answer to three decimal places 1 719 X c Determine the p value Round your answer to four decimal places d Test the above hypotheses Let a 0 05 O Reject Ho There is sufficient evidence to conclude that 0 Do not reject Ho There is insufficient evidence to conclude that 0 O Reject Ho There is insufficient evidence to conclude that 0 O Do not reject Ho There is sufficient evidence to conclude that H 0

Now we are to find the probability of receiving 10 calls in a 20 minute interval It is given that on average 36 calls are received per hour so this must be converted to a 20 minute interval We previously found that on average there are 0 6 calls per minute To find the mean number of calls in a 20 minute interval multiply the mean number of calls per minute by 20 20 minutes mean number of calls per minute 200 6 calls per 20 minutes Thus on the same 20 minute time interval we have Submit Skip you cannot come back Need Help Read It 12 Submit Answer 0 6 and x

According to a research center 13 of all merchandise sold in a particular country gets returned A department store in a certain city sampled 80 items sold in January and found that 20 of the items were returned a Construct a point estimate of the proportion of items returned for the population of sales transactions at the store in the given city b Construct a 95 confidence interval for the proportion of returns at the store in the given city Round your answers to four decimal places to c Is the proportion of returns at the store in the given city significantly different from the returns for the country as a whole Provide statistical support for your answer Develop appropriate hypotheses such that rejection of Ho will support the conclusion that the proportion of returns at the store in the given city is significantly different from the returns for the country as a whole Ho P 0 13 H P 0 13 Ho P 0 13 Ha P 0 13 Ho P 0 13 H P 0 13 Ho P 0 13 H P 0 13 Ho P 0 13 H p 0 13 Find the value of the test statistic Round your answer to two decimal places Find the p value Round your answer to four decimal places p value At a 0 01 what is your conclusion O Reject Ho There is insufficient evidence to conclude that the return rate for the store in the given city is different than the country s national return rate O Reject Ho There is sufficient evidence to conclude that the return rate for the store in the given city is different than the country s national return rate O Do not reject Ho There is sufficient evidence to conclude that the return rate for the store in the given city is different than the country s national return rate ufficient quidance to conclude that the return rate for the store in the given city is different than the country s national return rate

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 Ha 0 68 X X What is the test statistic Round your answer to two decimal places 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 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 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

Which of the following is NOT a requirement to satisfy the conditions for ANOVA All samples are dependent of one another Each group represents a simple random sample from its respective population The population have the same variance The population are normally distributed

When using a chi square test of independence what percent of the cells in the contingency table must have expected frequencies greater than 5 at least 50 at least 60 at least 70 at least 80

12 66 of adults cannot name a supreme court justice You randomly select five adults and ask each if they can name any of the justices The random variable represents the number of adults who cannot name a Supreme Court justice Complete parts a through d bel a Find the mean of the binomial distribution Round to two decimal places as needed p b Find the variance of the binomial distribution 0 Round to two decimal places as needed c Find the standard deviation of the binomial distribution Round to two decimal places as needed d What values of the random variable would you consider unusual Explain your reasoning On average out of 5 adults cannot name a supreme court justice with a standard deviation of because their probabilities are 1 0 05 Type integers or decimals rounded to two decimal places as needed 1 O less than O equal to more than adults The values x 0 and x would be unusual

rounding the result to two decimal places P Po Z Po 1 PO n 0 82 0 85 1 06 0 85 10 85 160 1 06 0 85 Step 7 A lower tail test is being performed so the area to the left of the test statistic z 1 06 is needed Use the standard normal table to find the p value for this test statistic rounding the result to four decimal places p value

Recall the previously determined values po 0 85 and n 160 Now we are to find the test statistic for a new sample proportion p 0 82 Use these values to find the test statistic rounding the result to two decimal places Z P Po Po 1 PO n 0 82 0 85 1 0 85 160 Submit Skip you cannot come back

The value for po is the hypothesized population proportion we are testing for Here we have po n 160 0 85 Z P Po Po 1 Po n 160 Step 2 Now that all of the values have been identified the test statistic can be calculated Use p 0 78 p 0 85 and n 160 to find the value of the z test statistic rounding the result to two decimal places 0 78 0 85 0 85 1 0 85 160 There was a sample of 160 items given so we have

unch to upd What percentage of the population live in their state of birth According to the U S Census Bureau s 2014 American Community Survey the figure ranges from 25 in Nevada to 78 7 in Louisiana The average percentage across all states and the District of Columbia is 57 7 The data in the file HomeState are consistent with the findings in this American Community Survey The data are for random sample of 120 Arkansas residents and for a random sample of 180 Virginia residents a Formulate hypotheses that can be used to determine whether the percentage of stay at home residents in the two states differs from the overall average of 57 7 O Ho P 0 577 H P 0 577 O Ho P 0 577 Ha P 0 577 Ho P 0 577 Ha p 0 577 Ho P 0 577 H P 0 577 Ho P 0 577 H P 0 577 b Estimate the proportion of stay at home residents in Arkansas Round your answer to four decimal places Does this proportion differ significantly from the mean proportion for all states Use a 0 05 Find the value of the test statistic Round your answer to two decimal places Find the p value Round your answer to four decimal places p value What is your conclusion O Reject Ho There is sufficient evidence to conclude that the proportion of stay at home residents in Arkansas differs from the overall proportion of 0 577 O Do not reject Ho There is insufficient evidence to conclude that the proportion of stay at home residents in Arkansas differs from the overall proportion of 0 577 O Reject Ho There is insufficient evidence to conclude that the proportion of stay at home residents in Arkansas differs from the overall proportion of 0 577 O Do not reject Ho There is sufficient evidence to conclude that the proportion of stay at home residents in Arkansas differs from the overall proportion of 0 577 c Estimate the proportion of stay at home residents in Virginia Round your answer to four decimal places all stator Use 0 05

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 H What is the test statistic Round your answer to two decimal places 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 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

You may need to use the appropriate appendix table or technology to answer this question At 95 confidence how large a sample should be taken to obtain a margin of error of 0 08 for the estimation of a population proportion Assume that past data are not available for devele planning value for p Round your answer up to the nearest whole number

a p 0 78 Before a p value can be found the test statistic must be calculated and the type of test must be determined The following hypotheses were given for a sample of 160 items and a sample proportion of p 0 78 Since this test is for a population proportion the z test statistic will be found This calculation is given below where p is the sample proportion Po is the hypothesized population proportion and n is the sample size Ho P 0 85 Ha P 0 85 Submit Z The value for po is the hypothesized population proportion we are testing for Here we have po Need Help P Po Po 1 PO n Skip you cannot come back Read It There was a sample of 160 items given so we have n

The null hypothesis Ho A states that the difference between sample means is statistically significant B states that the difference between sample means is due to the independent variable D cannot be tested directly states that the difference between sample means is due to chance I

The four characteristics of distributions are A central tendency variability skewness and kurtosis B range sum of squares variance and standard deviation nominal ordinal interval and ratio D measurement probability standard scores and symmetry

When two outcomes cannot both be true they are said to be A mutually exclusive B exhaustive C significant D skewed

Which of the following is not a criterion of relatedness A participants are randomly assigned to treatment groups B participants are related by blood genetic matching participants are matched on some critical variable D participants are tested before and after some experimental manipulation

3 pts We want to construct a 90 confidence interval estimating the average resting heart rate for a newborn baby If the population standard deviation is o 19 beats per minute and we want the margin of error for our confidence interval to be under 4 beats per minute our confidence interval shouldn t be wider than 8 beats per minute What is the minimum sample size we should collect

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 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

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

5 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

1 Twelve percent of people in a city eligible to donate blood actually do You randomly select four eligible blood donors and ask them if they donate blood Complete parts a through d below a Find the mean of the binomial distribution H b Find the variance of the binomial distribution 0 Round to the nearest hundredth as needed Round to the nearest hundredth as needed c Find the standard deviation of the binomial distribution 0 Round to the nearest hundredth as needed d Interpret the results in the context of the real life situation On average eligible adult s out of every 4 gives blood The standard deviation is four eligible adults the number of adults who donate blood would differ from the average number by no more than Type integers or decimals rounded to the nearest hundredth as needed so in most samples of