1.Suppose that the Smith CPA firm in Chicago claims that its clients receive different tax refunds, on average, than clients of its competitor, Jones and Company CPA, located on the other side of Chicago. To test the claim, 30 clients from the Smith firm are randomly selected and found to have a mean tax refund of $942 with a standard deviation of $103. At Jones and Company, a random sample of 35 clients were surveyed and found to have a mean refund of $898 with a standard deviation of $95. Test the claim made by the Smith firm at the 0.05 level of significance. (a) What are the null hypothesis and alternative hypothesis? (b) Check that the conditions for the normal distribution apply. (c) Use StatCrunch to get the p-value of the test. What is the p-value? (d) Write the conclusion of the test. use = 0.05 (e) Find the confidence intervals for the difference between means, using StatCrunch. (f) Interpret the Confidence intervals.

2. A clinic provides a program to help their clients lose weight and asks a consumer agency to investigate the effectiveness of the program. The agency takes a random sample of 30 people, weighing each person in the sample before the program begins and 3 months later. The p-value of the hypothesis test is <0.0001. Determine whether the program is effective. Hint: (a) What are the null hypothesis and alternative hypothesis? (b) Check that the conditions for the normal distribution apply. (c) Can we reject the null hypothesis? use = 0.05