Project A: Hypothesis Testing for Two Population Parameters
Choose one of the three questions to answer, collect data from members of the appropriate population, and perform a hypothesis test to answer the question. After you have written your conclusion, look at the "truth" and determine if your hypothesis test produced a correct decision, a Type I error, or a Type II error.
Pick one of the following questions to test:

Is there a difference in study habits for college students who are $25$ and older versus those students who are aged $18$$24$? Ask at least $30$ students $25$ and older and at least $30$ students aged $18$$24$ to estimate the amount of time they spend studying each week. Assume that the population variances are equal. Use a $0.10$ level of significance.

Do college freshmen spend less money each week eating out than seniors? Ask between $10$ and $20$ freshmen and between $10$ and $20$ seniors to estimate the amount of money they spend each week eating out. Assume that the population variances are different and both population distributions are approximately normal. Use a $0.05$ level of significance.

Are the percentages of students and faculty who exercise regularly the same? Ask at least $30$ students and at least $30$ faculty if they exercise at least three times per week. Record the number of students and the number of faculty who say "yes." Use a $0.01$ level of significance.
Step 1: State the null and alternative hypotheses.
What are the null and alternative hypotheses?
Step 2: Determine which distribution to use for the test statistic, and state the level of significance.
Based on the description of the test you chose, what formula should be used for the test statistic? Also, state the level of significance for your hypothesis test.
Step 3: Gather data and calculate the necessary sample statistics.
Collect data on the claim from the appropriate populations. Discuss which method of data collection you used. List any potential for bias. Calculate the sample statistics needed in order to compute the test statistic.
Calculate the test statistic using your sample statistics.
Step 4: Draw a conclusion and interpret the decision.
Determine the type of your hypothesis test: lefttailed, righttailed, or twotailed.
State the decision rule in terms of either the pvalue or the rejection region for the test statistic.
What is your conclusion? Be sure to answer the original question.
Types of Errors
Suppose the "truths" are as follows.

The mean amount of time spent studying each week is higher for students 25 and older in college than for college students aged 1824.

The mean amount of money spent eating out each week is higher for freshmen than for seniors.

The percentage of students who exercise at least three times per week is the same as the percentage of faculty.
Based on your conclusion, did you make a Type I error, Type II error, or a correct decision? Explain.