# 8 Hypothesis Testing Questions

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1) In a Gallup survey, 1087 randomly selected adults were asked "Do you have occasion to use alcoholic beverages such as liquor, wine, or beer, or are you a total abstainer?" Sixty-two percent of the subjects said that they used alcoholic beverages. Consider a hypothesis test that uses a 0.05 significance level to test the claim that the majority (more than 50%) of adults use alcoholic beverages.

a. What is the test statistic?

b. What is the critical value?

c. What is the P-value

d. What is the conclusion?

e. Based on the preceding results, can we conclude that 62% is significantly greater than 50% for all such hypothesis tests? Why or why not?

2) In the following questions test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

a. In a clinical tests of the drug Lipitor, 863 patients were treated with 10 mg doses Lipitor, and 19 of those patients experienced flu symptoms. Use a 0.01 significance level to test the claim that the percentage of treated patients with flu symptoms is greater than 1.9% rate for patients not give the treatments. Does it appear that flu symptoms are an adverse reaction of the treatment?

b. A simple random sample of households with TV sets in use shows that 1024 of them were tuned to 60 Minutes while 3836 were tuned to some other show. Use a 0.025 significance level to test the claim of a CBS executive that 60 Minutes gets more than a 20 share, which means that more than 20% of the sets in use are tuned to 60 minutes. If you are a commercial advertiser and you are trying to negotiate lower costs, what would you argue?

c. A television executive claims that fewer than half of all adults are annoyed by the violence shown on television. Sample data from a Roper poll showed that 48% of 1,998 surveyed adults indicated their annoyance with television violence. Use a 0.05 significance level and interpret. Is the executive's claim supported by the sample data?

3) Determine whether the given conditions justify using the methods when testing a claim about the population mean µ.

a. The sample size is n = 7, sigma is not known, and the original population is normally distributed.

b. The sample size is n = 47, sigma = 12.6, and the orginal population is not normally distributed.

4) Find the test statistic, p-value, critical values, and state the final conclusion

a. Claim: The mean starting salary for college graduates who have taken a statistics course is equal to $46,000.

Sample data: n = 65, x = $45,678. Assume that sigma = $9900 and the significance level is alpha = 0.05.

5) Find a range of numbers for the P-value

a. Left-tailed test with n = 12 and test statistic t = -0.855

b. Two-tailed test with n = 9 and test statistic t = -1.577

6) Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, p-value, critical values and state conclusion.

a. Claim: The mean starting salary for college graduates who have taken a statistics course is equal to $46,000.

Sample data: n = 27, x = $45,678, s = $9900. The significance level is alpha = 0.05.

7) Find the test statistic, find critical values of x^2 and limits containing the P-value, then determine whether there is sufficient evidence to support the given alternative hypothesis.

a. H1: sigma>12, alpha = 0.01, n = 5, s= 18

b. H1: sigma> 4.0, alpha = 0.05, n = 81, s =4.7

8) Survey Proves that Most American don't cheat on taxes. In Every Day is Saturday, a magazine for retired people, it was reported that a survey of 250 randomly selected subjects included 55% who said that they don't cheat when it come so paying their taxes. The magazine printed the survey in its March issue, and the 250 responses were randomly selected from the surveys that were mailed in by readers The first question on the survey asked "Do you cheat on your taxes or are you honest?" The magazine stated that its encouraging to learn that most Americans are honest at least when it comes to filling out their tax forms.

Using the above information answer the questions related to Chi Square Distribution

a) Test the claim that most Americans don't cheat on taxes. What do you conclude? Is it possible for any survey results to prove that most Americans don't cheat on their taxes?

b) Apart from the results of the hypothesis test, there are at least four other important issues that affect the validity of the survey results. Identify the other issues and describe how they affect the validity of the results.

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The solution answers 8 hypothesis testing word problems in a .doc file.

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1) In a Gallup survey, 1087 randomly selected adults were asked "Do you have occasion to use alcoholic beverages such as liquor, wine, or beer, or are you a total abstainer?" Sixty-two percent of the subjects said that they used alcoholic beverages. Consider a hypothesis test that uses a 0.05 significance level to test the claim that the majority (more than 50%) of adults use alcoholic beverages.

a. What is the test statistic?

Solution:

Since there are more than 30 samples we have to large sample test and the Z-test statistics for proportions.

Z =

b. What is the critical value?

Solution:

Since the level of significance is 0.05 and one tailed test, we have the value from the Z- Standard Normal Table is 1.64.

c. What is the P-value?

Solution:

The P-Value is

Z = = 5.576

P-value for this Z = 5.576 will be zero.

d. What is the conclusion?

Solution:

Since the table value of Z is less than the calculated value of Z, we have to accept the claim that there are more than 52% of the subjects use alcoholic beverages.

e. Based on the preceding results, can we conclude that 62% is significantly greater than 50% for all such hypothesis tests? Why or why not?

Solution:

Yes we can conclude that 62% is significantly greater than 50% .Since Z value is much greater, which is not less than any of the values in the Z-table.

2) In the following questions test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

a. In a clinical tests of the drug Lipitor, 863 patients were treated with 10 mg doses Lipitor, and 19 of those patients experienced flu symptoms. Use a 0.01 significance level to test the claim that the percentage of treated patients with flu symptoms is greater than 1.9% rate for patients not give the treatments. Does it appear that flu symptoms are an adverse reaction of the treatment?

Solution:

Null Hypothesis:

The percentage of treated patients with flu symptoms is less than or equal to 1.9% rate for patients not given the treatments.

Alternate Hypothesis:

The percentage of treated patients with flu symptoms is greater than 1.9% rate for patients not given the treatments.

Critical Value:

Since the test is one sided the Z-critical value for 0.01 level of significance is 2.33.

Test Statistics:

The test statistics is,

Z = = = = 0.20

P-Value:

P-Value = 1-0.5793 = 0.4207

Conclusion:

Since the P-Value is greater than the 0.01, we can conclude that we have to accept the null hypothesis.

Claim:

Since the null hypothesis the percentage of treated patients with flu symptoms is less than or equal to 1.9% rate ...

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