A researcher wants to test to see if husbands are significantly older than their wives. To do this, he collects the ages of husbands and pairs them with the ages of their respective wives for a random set of married couples. Suppose that data were collected for a random sample of 12 couples, where each difference is calculated by subtracting the age of the wife from the age of the husband. Assume that the ages are normally distributed. The test statistic is t≈1.434, α=0.05, the corresponding rejection region is t>1.796, the null hypothesis is H0:μd=0, and the alternative hypothesis is Ha:μd>0. Which of the following statements are accurate for this hypothesis test in order to evaluate the claim that the true mean difference between the age of the husband and the age of the wife is greater than zero? Select all that apply: A) Reject the null hypothesis that the true mean difference between the age of the husband and the age of the wife is equal to zero. B) Fail to reject the null hypothesis that the true mean difference between the age of the husband and the age of his respective wife is equal to zero. C) Based on the results of the hypothesis test, there is not enough evidence at the α=0.05 level of significance to suggest that the true mean difference between the age of the husband and the age of his respective wife is greater than zero. D) Based on the results of the hypothesis test, there is enough evidence at the α=0.05 level of significance to suggest that the true mean difference between the age of the husband and the age of his respective wife is greater than zero.
A researcher wants to test to see if husbands are significantly older than their wives. To do this, he collects the ages of husbands and pairs them with the ages of their respective wives for a random set of married couples. Suppose that data were collected for a random sample of 12 couples, where each difference is calculated by subtracting the age of the wife from the age of the husband. Assume that the ages are
Which of the following statements are accurate for this hypothesis test in order to evaluate the claim that the true mean difference between the age of the husband and the age of the wife is greater than zero?
Select all that apply:
A) Reject the null hypothesis that the true mean difference between the age of the husband and the age of the wife is equal to zero.
B) Fail to reject the null hypothesis that the true mean difference between the age of the husband and the age of his respective wife is equal to zero.
C) Based on the results of the hypothesis test, there is not enough evidence at the α=0.05 level of significance to suggest that the true mean difference between the age of the husband and the age of his respective wife is greater than zero.
D) Based on the results of the hypothesis test, there is enough evidence at the α=0.05 level of significance to suggest that the true mean difference between the age of the husband and the age of his respective wife is greater than zero.
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