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Wilcoxon: Hypothesis Testing and Finding P-Values

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Use the Wilcoxon signed-rank test to perform the required hypothesis test.

1) In 1995, the median age of the residents of one city was 36 years. A random sample taken this year of 10 residents of the town yielded the following ages in years.

5 28 37 49 30
68 11 58 40 34

At the 0.05 significance level, do the data provide sufficient evidence to conclude that the median age of the residents this year is different from the 1995 median age of 36 years?

a) What is the p-value for this test?
b) What is your decision (Reject/Fail to reject)?
Provide an appropriate response.

2) Suppose that you wish to perform a hypothesis test for a population mean. Suppose that the population standard deviation is unknown and the sample size is small. If the distribution of the variable under consideration is symmetric multimodal, should you use a t-test, a Wilcoxon signed-rank test, or neither?

A) Wilcoxon signed-rank test
B) t-test
C) Neither

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This solution performs a hypothesis test using the Wilcoxon signed-rank test.

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