Review Exercises (week 11: Hypothesis Testing with one Sample)

Review Exercises ( week 11: Hypothesis Testing with one Sample)

In Exercises 1-4, use the given claim to state null and a alternative hypothesis. Identify which hypothesis represents the claim.

1. Claim:	2. Claim:
3. Claim:	4. Claim:

In Exercises 5 8, do the following.

(a) State the null and alternative hypotheses.

(b) Determine when a type I or type II error occurs for a hypothesis test.

(c) Determine whether the hypothesis test is a left-tailed test, a right-tailed test, or a two-tailed test. Explain your reasoning.

(d) How should you interpret a decision that rejects the null hypothesis?

(e) How should you interpret a decision that fails to reject the null hypothesis?

1. An organization believes that the proportion of American adults who use nonprescription pain relievers is 85%.

1. A tire manufacture guarantees that the mean life of a certain type of tire is at least 30,000 miles.

1. A soup maker says that the standard deviation of the sodium content in one serving of a certain soup is no more that 50 milligrams.

1. A cereal maker claims that the mean number of fat calories in one serving of its cereal is less than 20.

In Exercises 9 – 12, find the critical value(s) for the indicated z-test with the level of significance α.

9. Left – tailed test, α = 0.02	10. Two-tailed test, α = 0.005
11. Right-tailed test, α = 0.025	12. Two-tailed test, α = 0.08

In Exercises 13 – 16, test the claim about the population mean µ with a z-test using the given sample statistics and level of significance α.

13. Claim: µ≤ 45; α = 0.05. Statistics:

14. Claim: Statistics:

15. Claim: Statistics:

16. Claim: Statistics:

In Exercises 17 and 18, use a P-value to test the claim about the population mean µ using the given sample statistics. State your decision for α = 0.10, α 0.05, and α = 0.01 levels of significance.

17. Claim: µ ≤ 0.05; Statistics:

18. Claim: Statistics:

In Exercises 19 – 22, find the critical value(s) for the t-test with the indicated sample size n and level of significance α.

19. Two-tailed test, n=20, α = 0.05.

20. Right-tailed test, n=8, α = 0.01.

21. Left-tailed test, n= 15, α = 0.10.

22. Two-tailed test, n=12, α = 0.025.

In Exercises 23 -26, test the claim about the population mean µ using the given sample statistics and level of significance α. Assume the population is normally distributed.

23. Claim: Statistics:

24. Claim: Statistics:

25. Claim; Statistics:

26. Claim: Statistics:

27. Use a t-test to investigate the claim. Assume each population is normally distributed.

A fitness magazine advertises that the average monthly cost of joining a health club is $25. You work for a consumer advocacy group and are asked to test this claim. You find that a random sample of 18 clubs has a mean monthly cost of $26.25 and a standard deviation of $3.23.

At α = 0.10, do you have enough evidence to reject the advertisement’s claim?

28. Use a t-statistic and its P-value to test the claim about the population mean µ using the given sample statistics. Assume the population is normally distributed.

A large university says the mean number of classroom hours per week for full-time faculty is more than 9. A random sample of the number of classroom hours for full-time faculty for one week is listed. At α = 0.05, test the university’s claim.

10.7 9.8 11.6 9.7 7.6 11.3 14.1 8.1 11.5 8.5 6.9

In exercises 30 – 33, decide whether the normal distribution can be used to approximate the binomial distribution. If it can, use the z-test to test the claim about the population proportion p for the given values and level of significance α.

30. Claim: p = 0.15; α = 0.05. Statistics:

31. Claim: p < 0.70; α = 0.01. Statistics:

32. Claim: p < 0.08; α = 0.05. Statistics: .

33. Claim: p=0.5; α = 0.10. Statistics:

35. Test the claim about the population proportion p.

A communications industry spokesperson claims that over 40% of Americans either own a cellular phone or have a family member that does. In a random survey of 1036 Americans, 456 said that they or a family member owned a cellular phone. Test the spo0kesperson’s claim at the α = 0.10 level. What can you conclude?

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