# Statistics and Hypothesis Testing Problems

1. True or False? A hypothesis test is a process that uses population parameters to test a claim

about about a sample statistics.

2. Use the given statement to represent a claim. Write its complement and state which is Ha and which is H0.

3. Determine whether the hypothesis test with the given null hypothesis listed below is lefttailed, right-tailed, or two-tailed.

H0 : = 100

Use the following information to answer questions 4-7.

Working Hours A company's shipping department claims that the average working hours per

week is greater than 44 hours.

4. Write the null hypothesis, H0.

5. Write the alternate hypothesis, Ha.

6. Which hypothesis is the claim?

7. What type of hypothesis test will be required?

Use the following information to answer questions 8 and 9.

Internet Users A study claims that the proportion, p, of adults in the United States that use

the internet is 68%.

8. Write a sentence describing a type I error for a hypothesis test of the claim above.

9. Write a sentence describing a type II error for a hypothesis test of the claim above.

Use the following information to answer questions 10 and 11.

Shipment Weights A postal worker claims that the average weight of all U.S. Postal parcel

shipments is greater than 5:6 pounds. Assume that a hypothesis test is conducted.

10. With regard to the claim, how should you interpret a decision that rejects the null hypothesis?

11. With regard to the claim, how should you interpret a decision that fails to reject the null

hypothesis?

Use the following information pertaining to a hypothesis test to answer questions 12 and

13. Test: right-tailed, z = 2:27,

= 0:01

12. Find the P-value for the hypothesis test.

13. Decide whether to reject H0 for the given level of significance

.

14. Suppose that a two-tailed hypothesis test is being conducted and the P-value is 0:0768. What

are the z-values that corresponds to this P-value?

15. Find the critical value for the indicated type of test and level of significance

.

Test: Left-tailed,

= 0:10.

Use the following information to answer questions 16-19.

Suppose that for a two-tailed hypothesis test the critical values are z0 = 1:88 and z0 =

1:88. State whether you would reject or fail to reject the null hypothesis if the standardized

test statistic z has the values listed below.

16. z = 1:72

17. z = 2:03

18. z = 1:65

19. z = 1:80

20. Test the claim about the population mean at the given level of significance

using the

given sample statistics. Claim: < 1000;

= 0:05; Sample statistics: x = 988, s = 29,

n = 50.

Section 7.3

For problems 21 and 22, use the value of

and n to and the critical value t0 for the

specified t-test.

21. Test: Left-tailed;

= 0:025; n = 17

22. Test: Two-tailed;

= 0:01; n = 23

23. Use a t-test to test the claim about the population mean at the given level of significance

using the given sample statistics.

Claim: = 640 6

= 0:05

Sample statistics: x = 643, s = 4:0, n = 10.

#### Solution Preview

1. True or False? A hypothesis test is a process that uses population parameters to test a claim

about a sample statistics.

False. The right one is a hypothesis is a process that uses sample statistics to test a claim about the value of a population parameter.

2. Use the given statement to represent a claim. Write its complement and state which is

Ha and which is H0.

238

Ho: the mean expenditure in the gas for a family is 238 dollars.

Ha: the mean expenditure in the gas for a family is not 238 dollars.

3. Determine whether the hypothesis test with the given null hypothesis listed below is lefttailed, right-tailed, or two-tailed.

H0 : = 100

This is two tailed since it gives no direction.

Use the following information to answer questions 4-7.

Working Hours A company's shipping department claims that the average working hours per

week is greater than 44 hours.

4. Write the null hypothesis, H0.

Ho Null hypothesis: the average working hours per week is equal or less than 44 hours. µ<=44.

5. Write the alternate hypothesis, Ha.

Ha: the average working hours per week is greater than 44 hours. µ>44

6. Which hypothesis is the claim?

Ha is the claim.

7. What type of hypothesis test will be required?

Since it is directional, it is one tailed (right tailed) t test.

Use the following information to answer questions 8 and 9.

Internet Users A study claims that the proportion, p, of adults in the United States ...

#### Solution Summary

The solution assists with answering the statistics and hypothesis testing problems.