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. Find the test statistic and degrees of freedom for an appropriate hypothesis test using the data set below. Let the difference d for each couple be computed as d = husband - wife. Assume that the ages are normally distributed. Round the test statistic to three decimal places. Husband Wife 42 39 44 43 46 42 51 48 34 30 36 38 62 59 47 50 64 58 41 44 50 51 54 50
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H0: μd = 0 The alternative hypothesis (Ha) is that husbands are significantly older than their wives, meaning that the mean difference (μd) is greater than zero. Ha: μd > 0 Show more…
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Are husbands, on average, older than their wives? A random sample of 30 married couples was taken to find the age difference, husband's age minus wife's age, at the date of marriage. The differences are listed below. Test to see if, when getting married, the husband is older than the wife on average. Marriage Age Difference Husband-Wife: The age differences are assumed to be normally distributed. Use a significance level of 5%. A. State the alternative hypothesis: HA: μd ≠ 0 μd < 0 μd > 0 B. State the mean of the sample: C. State the standard error of the sample means: D. State the test statistic: t = E. State the p-value: F. Decision: Fail to reject the null hypothesis. Reject the null hypothesis.
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The U.S. Census Bureau collects data on the ages of married people. Suppose that eight married couples are randomly selected and have the ages given in the following table. Determine the 90% confidence interval for the true mean difference between the ages of married males and married females. Let d=(age of husband)−(age of wife). Assume that the ages are normally distributed for the populations of both husbands and wives in the U.S. Husband 26 56 54 61 48 56 41 60 Wife 27 64 46 66 54 52 39 63 Step 1 of 4: Find the mean of the paired differences, d‾d‾. Round your answer to one decimal place. Step 2 of 4: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places. Step 3 of 4: Find the standard deviation of the paired differences to be used in constructing the confidence interval. Round your answer to one decimal place. Step 4 of 4: Construct the 90%90% confidence interval. Round your answers to one decimal place.
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The U.S. Census Bureau collects data on the ages of married people. Suppose that eight married couples are randomly selected and have the ages given in the following table. Determine the 98% confidence interval for the true mean difference between the ages of married males and married females. Let d = (age of husband) - (age of wife). Assume that the ages are normally distributed for the populations of both husbands and wives in the U.S. Husband: 30, 52, 43, 55, 39, 44, 64, 32 Wife: 32, 42, 46, 54, 49, 49, 68, 26 Step 1 of 4: Find the mean of the paired differences, d. Round your answer to one decimal place. Step 2 of 4: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places. Step 3 of 4: Find the standard deviation of the paired differences to be used in constructing the confidence interval. Round your answer to one decimal place. Step 4 of 4: Construct the 98% confidence interval. Round your answers to one decimal place.
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