1. The average price of homes sold in the U.S. in the past year was $220,000. A random sample of 81 homes sold this year showed a sample mean price of $210,000. It is known that the standard deviation of the population is $36,000. Using a 1% level of significance, test to determine if there has been a significant decrease in the average price homes. Use the p value approach. Make sure to show all parts of the test, including hypotheses, test statistic, decision rule, decision and conclusion.
2. A sample of 30 cookies is taken to test the claim that each cookie contains an average of at least 9 chocolate chips. The average number of chocolate chips per cookie in the sample was 7.8 with a sample standard deviation of 3. Using a 5% level of significance, perform the hypothesis test using the critical value approach. Show all parts of the test, including hypotheses, test statistic, decision rule, decision and conclusion.