Ch. 13 (13.3)

Which of the following is NOT true of the Wilcoxon​ signed-ranks test?

The Wilcoxon​ signed-ranks test uses only the signs of the differences.

Which of the following is NOT a requirement for the Wilcoxon​ signed-ranks test for matched​ pairs?

The data have a normal distribution.

The​ ________________ is a nonparametric test that uses ranks for testing a null hypothesis that the population of matched pairs has differences with a median equal to​ zero, or testing a null hypothesis that a single population has a claimed value of the median.

Wilcoxon signed-ranks test

The table below lists weights of college students in September and later in April of their freshman year. Assume the use of the Wilcoxon​ signed-ranks test to test the claim of no difference between September weights and April weights. What requirements must be satisfied for this​ test? Is there any requirement that the populations must have a normal distribution or any other specific​ distribution? In what sense is this Wilcoxon​ signed-ranks test a​ "distribution-free test"?

The only requirements are that the matched pairs are a simple random sample and the population of differences has a distribution that is approximately symmetric. There is no requirement of a normal distribution or any other specific​ distribution, which is why the test is a​ "distribution-free test."

The amounts​ (in oz) in cans of soda are given below. The cans are labeled to indicate that the contents are 12 oz of soda. Use a 0.01 significance level to test the claim that the cans are filled so that the median amount is 12 oz. If the median is not 12​ oz, are consumers being​ cheated? a. First define the null and alternative hypotheses. b. Calculate the Wilcoxon test statistic. c. Since the sample size n is greater than​ 30, convert T to a z test statistic. d. Determine the critical​ value(s). e. Choose the correct answer below. f. Are consumers being​ cheated?

a. H0​: The median amount of soda is equal to 12 oz. H1​: The median amount of soda is not equal to 12 oz. b. T= 123.5 c. z= 3.14 d. CV= -2.58, 2.58 e. Reject H0. There is sufficient evidence to warrant rejection of the claim that the median amount of soda is 12.0 oz. f. Since the median of the sample is 12.1, there is no reason to suspect that consumers are being cheated.

he amounts​ (in oz) in cans of soda are given below. The cans are labeled to indicate that the contents are 12 oz of soda. Use a 0.01 significance level to test the claim that the cans are filled so that the median amount is 12 oz. If the median is not 12​ oz, are consumers being​ cheated? a. First define the null and alternative hypotheses. b. Calculate the Wilcoxon test statistic. c. Since the sample size n is greater than​ 30, convert T to a z test statistic. d. Determine the critical​ value(s). e. Choose the correct answer below. f. Are consumers being​ cheated?

a. H0​: The median amount of soda is equal to 12 oz. H1​: The median amount of soda is not equal to 12 oz. b. T= 82 c. z= 3.68 d. CV= -2.58, 2.58 e. Reject H0. There is sufficient evidence to warrant rejection of the claim that the median amount of soda is 12.0 oz. f. Since the median of the sample is 12.1, there is no reason to suspect that consumers are being cheated.

Listed below are actual high temperatures and the high temperatures forecast one day in advance. Use a 0.05 significance level to test the claim that the population of differences has a median of zero. What do the results suggest about the accuracy of the​ predictions? a. What are the hypotheses for this​ test? b. What is the test​ statistic? c. The critical value is? d. What is the​ conclusion?

a. H0​: The median of the differences equals zero. H1​: The median of the differences is not equal to zero. b. T= 6.5 c. CV= 1 d. There is not enough evidence to warrant rejection of the claim that the population of differences has a median of zero. Based on the sample​ data, it appears that the predictions are reasonably accurate.

Researchers collected data on the numbers of hospital admissions resulting from motor vehicle​ crashes, and results are given for Friday the 6th and Friday the 13th in the same month. Use the Wilcoxon​ signed-ranks test to test the claim that the matched pairs have differences that come from a population with median equal to zero at a significance level of α=0.05. a. First define the null and alternative hypotheses. b. Calculate the test statistic. c. Calculate the critical value. d. What is the conclusion for this hypothesis​ test?

a. H0​: The population of differences has a median equal to 0. H1​: The population of differences has a median not equal to 0. b. T= 9.5 c. CV= 1 d. Fail to reject H0. There is insufficient evidence to warrant rejection of the claim of no difference.

The accompanying table lists the​ "attribute" ratings made by a sample of participants in a speed dating session. Each attribute rating is the sum of the ratings of five attributes​ (sincerity, intelligence,​ fun, ambition, shared​ interests). Use the Wilcoxon​ signed-ranks test to test the claim that the matched pairs have differences that come from a population with a median equal to zero. Use a 0.01 significance level. a. Determine the null and alternative hypotheses. b. The test statistic is c. The​ P-value is d. State the conclusion to the hypothesis test.

a. H0​: There is no difference between female attribute ratings and male attribute ratings. H1​: There is a difference between female attribute ratings and male attribute ratings. b. T= 2345 c. P-value= 0.952 d. There is not sufficient evidence to warrant rejection of the claim of no difference. There is not sufficient evidence to support the claim that there is a difference between female attribute ratings and male attribute ratings.