A commuter train arrives punc- tually at a station every half hour. Each morning, a commuter...

 

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A commuter train arrives punc- tually at a station every half hour. Each morning, a commuter named John leaves his house and casually strolls to the train sta- tion. John thinks that he is unlucky and that he waits longer for the train on average than he should. a. Assuming that John is not unlucky, how long should he expect to wait for the train, on average? b. Assuming that John is not unlucky, identify the distribution of the times he waits for the train. c. The following is a sample of the times, in minutes, that John waited for the train. 24 26 20 3 19 28 22 4 11 5 16 24 Use the Wilcoxon signed-rank test to decide, at the 10% sig- nificance level, whether the data provide sufficient evidence to conclude that, on average, John waits more than 15 minutes for the train. d. Explain why the Wilcoxon signed-rank test is appropri- ate here. e. Is the Wilcoxon signed-rank test more appropriate here than the t-test? Explain your answer. A commuter train arrives punc- tually at a station every half hour. Each morning, a commuter named John leaves his house and casually strolls to the train sta- tion. John thinks that he is unlucky and that he waits longer for the train on average than he should. a. Assuming that John is not unlucky, how long should he expect to wait for the train, on average? b. Assuming that John is not unlucky, identify the distribution of the times he waits for the train. c. The following is a sample of the times, in minutes, that John waited for the train. 24 26 20 3 19 28 22 4 11 5 16 24 Use the Wilcoxon signed-rank test to decide, at the 10% sig- nificance level, whether the data provide sufficient evidence to conclude that, on average, John waits more than 15 minutes for the train. d. Explain why the Wilcoxon signed-rank test is appropri- ate here. e. Is the Wilcoxon signed-rank test more appropriate here than the t-test? Explain your answer.

Answer rating: 100% (QA)

To address the question we need to perform the Wilcoxon signedrank test on the provided data The Wilcoxon signedrank test is a nonparametric statistical test that compares the median of a single sample to a specified value in this case 15 minutes the expected wait time if John is not unlucky Here are the data points from the image 24 20 3 19 28 22 26 4 11 5 16 24 First we will follow the steps for performing the Wilcoxon signedrank test 1 Calculate the differences between the observed times and the median value were testing against 15 minutes 2 Rank the absolute values of these differences ignoring the sign the smallest difference gets rank 1 the next smallest rank 2 and so on 3 Sum the ranks for the differences that are positive and those that are negative separately 4 The test statistic ... View the full answer