A student researcher compares the heights of men and women from the student body

Question

A student researcher compares the heights of men and women from the student body of a certain college in order to estimate the difference in their mean heights. A random sample of 12 men had a mean height of 69.9 inches with a standard deviation of 2.93 inches. A random sample of 17 women had a mean height of 66.9 inches with a standard deviation of 2.55 inches. Determine the 90% confidence interval for the true mean difference between the mean height of the men and the mean height of the women. Assume that the population variances are equal and that the two populations are normally distributed.

Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval.

Step 2 of 3: Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 3 of 3: Construct the 90% confidence interval. Round your answers to two decimal places.

Explanation / Answer

The statistical software output for this problem is:

Two sample T summary confidence interval:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
(with pooled variances)

90% confidence interval results:

Hence,

1. Point estimate = 3

2. Margin of error = (4.741173 - 1.258827)/2 = 1.741173

3. 90% confidence interval: (1.26, 4.74)

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