Homework: Hypothesis Testing

1) A random sample of 100 observations from a population with standard deviation 60 yielded a sample mean of 110.
a) Test the null hypothesis that u≤100 against the alternative hypothesis that u > 100. Assume we want 95% confidence.
b) Test the null hypothesis that u=100 against the alternative hypothesis that u ≠ 100. Again, assume 95% confidence. c) Compare the results of the two tests you conducted. Explain why the results differ.

2) BusinessWeek.com provides consumers with retail prices of new cars at dealers from across the country. The July 2006 prices for the hybrid Toyota prius were obtained from a sample of 160 dealers. These 160 prices are saved in the “Hybrid cars” file.
a) Give the null and alternative hypothesis for testing whether the mean July 2006 dealer price of the Toyota Prius, u, differs from $25,000. b) Access the hybridcars file and find the sample mean and sample standard deviation. c) Use the information in part b to find a test statistic for the hypothesis test. d) Give the rejection region using the hypothesis test, using α=.05. e) State the appropriate conclusion for the hypothesis test.

3) What is a p-value measuring? Suppose in excel (we will see this a lot very soon), we get a p-value of .001. What does this mean? What would a p-value of .23 mean?
4) The director of a state agency believes that the average starting salary for clerical employees in the state is less than $30,000 per year. To test her hypothesis, she has collected a simple random sample of 100 starting clerical salaries from across the state and found that the sample mean is $29,750.
a) State the appropriate null and alternative hypothesis.
b) Assuming the population standard deviation is known to be $2,500 and the significance level for the test is to be 0.05, what is the