Study carefully Example 10.15 (starting on p. 478). Suppose the data analyst sus
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Question
Study carefully Example 10.15 (starting on p. 478). Suppose the data analyst suspects that the difference in age between couples is not normally distributed. What can she do?
perform the Wilcoxon signed rank test
perform the Mann Whitney test
perform the two-sample t-test since the sample size is large enough
a.perform the Wilcoxon signed rank test
b.perform the Mann Whitney test
c.perform the two-sample t-test since the sample size is large enough
d.perform the paired t-test since the sample size is large enough
EXAMPLE 10.15 comparing Two Means, Using a Paired Sample Ages of Married People The U.S. Census Bureau publishes information on ages of married people in Current Population Reports. Suppose that we wan decide whether, in the United States, the mean age of married men mean age of married women. a. Formulate the problem statistically by posing it as a hypothesis te b. Explain the basic idea for carrying out the hypothesis test. c. Suppose that 10 married couples in the United States are selected and that the ages, in years, of the people chosen are as shown in the second ecisio concerning the hypothesis test. TABLE 10.13 Couple Husband Wife Difference, d Ages, in years, of a random sample of 10 married couples 22 33 36 64 33 67 41 13 36Explanation / Answer
Answer is B
T test or any test requiruing the normal distribution assumption is out of question. Givrn sample of only 10, the test is ruled out. C and D are out.
The Mann–Whitney U test is a nonparametrictest of the null hypothesis that it is equally likely that a randomly selected value from one sample will be less than or greater than a randomly selected value from a second sample. But this is not we want.
Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used when comparing two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e. it is a paired difference test). It can be used as an alternative to the paired Student's t-test, t-test for matched pairs, or the t-test for dependent samples when the population cannot be assumed to be normally distributed.This is what we want and should be used.