1. A research study looks to examine spending in grocery stores that play music. The hypothesis is that stores that play music increase average sales. A random sample of 100 transactions from stores that play music yielded a sample mean sales of $175 per transaction. Assume from previous research that the population standard deviation is $28. The test should determine if sales are greater than

$174.3. Let = .05.

1. Describe the Type I error associated with this problem.
2. Determine the correct null and alternative hypotheses for a test to determine if music increased average sales above $170 per transaction.

Ho : Ha :

1. Report and interpret the p-value and test statistic (z-value) from this test. What is the underlying distribution for the sample mean in this case?
2. Let = 0.05. What is the conclusion of your test? Does the evidence suggest that music increases sales on average? Explain.

1. In the U.S court system defendants are innocent until proven guilty. A not guilty verdict, or presumption of innocence, can be thought of as the status quo. While, with enough evidence a defendant can be considered guilty. In some cases this is referred to as, "beyond a reasonable doubt" and is quantified as more than an 85% likelihood someone is guilty. Use this information to answer the following questions.

1. Develop an appropriate null and alternative hypothesis to determine if there is enough evidence for a guilty conviction. You can use numbers or words to describe the null and alternative.

H0 :

Ha :

1. Describe the Type-I error associated with this problem. Be very specific in relation to this problem. Explain what level of you would choose knowing the consequences from this type of error.
2. Describe the Type-II error associated with this problem. Be very specific in relation to this problem.

1. A recent study wants to examine the amount of student loan debt students are graduating with. Ten years ago students graduated with an average student loan debt equal to $21,600. Use the worksheet "student loans" to answer the following questions. There are 25 observations of student loan debt from recent college graduates.

1. Construct a 95% Confidence Interval around the population mean student loan debt. Report the upper and lower bounds and interpret this interval.
2. The researcher wants to determine if students are graduating with a different amount of student loan debt than $21,600. Specify the correct null and alternative hypotheses corresponding to this problem.

Ho : Ha :

1. Describe the Type I error associated with this question.
2. Let = 0.05. What is the conclusion of the test? Should there be a concern about the amount of student loan debt held by recent graduates? Justify the conclusion that you have suggested.

1. Aggregate student loan debt for the class of 2016 set a record at $1.45 Trillion. In comparison, 2006 student loan debt was $445 Billion. The media tends to highlight this difference, but they often fail to recognize that there were roughly 44 million Americans with student loan debt in 2016 compared with only 20 million Americans in 2006. Use the worksheet "loans" to analyze the difference in average student loan debt per student. The data set includes observations from two random samples of loan debt for students in 2006 and 2016.

1. We are interested in testing if the average student loan debt per student in 2016 exceeds average student loan debt in 2006. Specify the null and alternative hypothesis for such a test.

H0 :

Ha :

1. What is the estimated difference in loan debt between the two years? Interpret this value.
2. Let = .10. Perform the hypothesis test. Report the p-value for the test. What is your conclusion from this test?

1. A statistical researcher is conducting a test to determine if females in finance positions earn less than men with equivalent jobs. After collecting income data for the two groups the researcher needs to determine the appropriate test to run in excel. Which test would you choose - a t-test assuming equal variances or a t-test assuming unequal variances? Would it be appropriate to use the t-test assuming unequal variances if the variance in income is the same between men and women? Explain this result.
2. One unfortunate characteristic of the financial crisis in 2008 was the duration for those who were unemployed. A study wanted to examine the difference in average weeks people were unemployed between the recession in 2001 and the recession in 2008. Use the worksheet "unemployed" to analyze the differences in average weeks people were unemployed.
3. Specify the null and alternative hypothesis for a test to determine if the average weeks of unemployment were greater during the recession in 2008 than in 2001.

Ho :

Ha :

1. What is the estimated difference in weeks unemployed between the two recessions?
2. Let = .05. Perform the hypothesis test. Report the p-value for the test. What is your conclusion from this test?
3. A study wants to determine if the returns from several mutual funds are different. A random sample of 10 observations for each fund was collected. The worksheet "Mutual Fund" contains observations for monthly returns over the last year.
4. Specify the null and alternative hypothesis for a test to determine if at least one fund performs differently from the others. Let = .01

H0 :

Ha :

1. Explain the conceptual difference in the ANOVA for the Between group and Within group variation.
2. Report the p-value and perform the test. What is the conclusion of the test? That is, is there enough evidence to suggest that the funds perform differently. Explain your answer.
3. Perform a hypothesis test to determine if the Fidelity Group fund performed better than the Vanguard Retirement fund. Use = 0.05. State your null and alternative hypothesis along with the p-value from the test. Explain the result.
4. The unemployment rate for Black Americans 16-19 years old is 24.3%. The unemployment rate for White Americans 16-19 years old is 11.3%. Fifty people were sampled in each population. Use this information to answer the following questions.
5. Construct a 95% confidence interval around the unemployment rate for Black Americans 16-19 years old. Report the upper and lower bounds.
6. Construct a 95% confidence interval around the unemployment rate for White Americans 16-19 years old. Report the upper and lower bounds.
7. Using the two confidence intervals as evidence, do you believe that the unemployment rate for Black Americans 16-19 years old is larger than the unemployment rate for White Americans 16-19 years old? Explain this result.
8. A recent study collected data on pizza sales in various cities around the country. The study wants to examine if pizza sales are higher in bigger cities. The dependent variable is sales (measured in millions of dollars). The independent variable is population (measured in 1,000's). Use the data set pizza to fit the following linear regression:

sales = 0 + 1population.

1. What is the estimate for the intercept? Interpret this value. Does this seem to provide a realistic value for the intercept?
2. What is the estimate for the slope (population effect)? Interpret this value.
3. Using = .05, specify the null and alternative hypothesis to determine if the slope is positive. Report the p-value and the result of the test. Does population have a significant effect on pizza sales? Explain.

H0 :

Ha :

Report the R2 and interpret this value. Explain if the regression model provides a good fit for the data.