Question

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?

Answer 1

Complete Question

The complete is shown on the first uploaded image

Answer:

The correct option are option 2 and option 4

Explanation:

From the question we are told that

The sample size is n = 12

The test statistics is
`t \approx 1.434`

The level of significance is
`\alpha = 0.05`

The rejection region is t>1.796

The null hypothesis
`H_o: \mu_d=0`

The alternative hypothesis is
`H_a : \mu_d >0`

From the given values we see that t < 1.796(i.e 1.434 < 1.796 ) which implies that t is not within the rejection region

Hence we fail to reject the null hypothesis

The conclusion is that there is insufficient evidence to suggest that that the husbands are significantly older than the wife.