1. Test whether .

2. Test whether .

3. Test whether is below zero.

1. Provide the null and alternative hypotheses.
2. Describe the two ways a correct decision could be made.
3. Describe what a Type I error would mean in the context of the problem.
4. Describe what a Type II error would mean in the context of the problem.

4. Household Size. The U.S. Census Bureau reported (2010) that the mean household size is 2.58 persons. We conduct a hypothesis test to determine whether the population mean household size has changed.

5. Speeding-Related Traffic Fatalities. The National Highway Traffic Safety Administration reports that the mean number of speeding-related traffic fatalities over the Thanksgiving holiday period from 1994 to 2003 was 202.7. We conduct a hypothesis test to examine whether the population mean number of such fatalities has decreased.

6. Salaries of Accounting Associate Professors. Salary.com reports that the mean salary for accounting associate professors in 2014 was $94,000. A hypothesis test was conducted to determine if the population mean salary of accounting associate professors has increased.

7.

8.

9.

1. Find the value of .
2. Find the critical-value rejection rule.
3. Draw a standard normal curve and indicate the critical region.
4. State the conclusion and interpretation.

10.

11.

12.

13. Credit Scores in Georgia. According to CreditReport. com, the mean credit score in Georgia in 2014 was 668. A random sample of 144 Georgia residents this year shows a mean credit score of 650. Assume . Perform a hypothesis test, using level of significance , to determine if the population mean credit score in Georgia has decreased.

1. State the hypotheses and the rejection rule for the -value method.
2. Calculate .
3. Find the -value. Draw the standard normal curve, with and the -value indicated on it.
4. State the conclusion and the interpretation.

14. We are interested in testing at level of significance whether the population mean differs from 500. A random sample of size 100 is taken, with a mean of 520. Assume .

15. We want to test, at level of significance , whether the population mean is less than −10. A random sample of size 25 is taken from a normal population. The sample mean is −12. Assume .

16. Sleeping During the Full Moon. A study found that subjects slept on average 20 minutes less on nights of the full moon than otherwise.²¹ Other researchers disagree and are interested in testing whether the mean difference in sleep is less than 20 minutes. A random sample of 100 subjects showed that they slept, on average, 10 minutes less on nights of the full moon than otherwise. Assume the population standard deviation is 15 minutes. Perform the appropriate hypothesis test using level of significance .

17.

18.

19.

20. Describe what happens to the critical value for right-tailed tests as decreases.

21. A random sample of size 16 from a normal population yields a sample mean of 10 and a sample standard deviation of 3. Test whether the population mean differs from 9, using level of significance .

22. A random sample of size 144 from an unknown population yields a sample mean of 45 and a sample standard deviation of 10. Test whether the population mean differs from 45, using level of significance .

1. Check the normality conditions.
2. State the hypotheses.
3. Find and the rejection rule.
4. Calculate .
5. State the conclusion and the interpretation.

23. Test whether the population proportion exceeds 0.8. A random sample of size 1000 yields 830 successes. Let .

24. Test whether the population proportion is below 0.2. A random sample of size 900 yields 160 successes. Let .

25. Test whether the population proportion is not equal to 0.4. A random sample of size 100 yields 55 successes. Let . For Exercises 26 and 27, do the following:

26. Test whether the population proportion differs from 0.7. A random sample of size 144 yields 110 successes.

27. Test whether the population proportion is less than 0.25. A random sample of size 100 yields 25 successes.

28. DSL Internet Service. The U.S. Department of Commerce reports that 41.6% of Internet users preferred DSL as their method of service delivery.²² A random sample of 1000 Internet users shows 350 who preferred DSL. If appropriate, test whether the population proportion who prefer DSL has decreased, using level of significance .

1. State the hypotheses.
2. Find the critical value or values, and state the rejection rule.
3. Find . Also, draw a distribution and indicate and the critical value or values.
4. State the conclusion and the interpretation.

29. We are testing whether and have a random sample of size 20 with a standard deviation of . Let .

30. We are testing whether and have a random sample of size 26 with a sample variance of 90. Let .

1. State the hypotheses and the -value rejection rule for .
2. Find .
3. Find the -value. Also, draw a distribution and indicate and the -value.
4. State the conclusion and the interpretation.

31. We are testing whether and have a random sample of size eight with a sample variance of 1200.

32. We are testing whether and have a random sample of size 26 with a standard deviation of .

1. Calculate the value or values of .
2. Draw a normal curve, centered at , with the value or values of indicated.
3. Calculate , the probability of a Type II error for that value of . Shade the corresponding area under the normal curve.
4. Calculate the power of the hypothesis test.

33.

34.

35.

36.

37.

38. Refer to Exercises 33–37. Construct the power curve for the given values of .