You have heard that if you leave your money in mutual funds for a longer period of time, you will see a greater return. So you would like to compare the 3-year and 5-year returns of a random sample of mutual funds to see if indeed, your return is expected to be greater if you leave your money in the funds for 5 years.

a) Using the data provided, check the conditions for this test.

b) Write the null and alternative hypotheses for this test.

c) Test the hypothesis and find the P-value if appropriate.

d) Find a 95% confidence interval for the mean difference.