Question

A student researcher compares the heights of American students and non-American students from the student body of a certain college in order to estimate the difference in their mean heights. A random sample of 17 American students had a mean height of 70.8 inches with a standard deviation of 1.99 inches. A random sample of 12 non-American students had a mean height of 63.3 inches with a standard deviation of 2.63 inches. Determine the 90% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students. Assume that the population variances are equal and that the two populations are normally distributed. Step 2 of 3 : Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Answer 1

A random sample of 17 American students had a mean height of 70.8 inches with a standard deviation of 1.99 inches. A random sample of 12 non-American students had a mean height of 63.3 inches with a standard deviation of 2.63 inches.

American Student sample

Number of American students in the random sample : sample size : n1 = 17

Sample mean height of American students : = 70.8

Sample standard deviation of height of American students : s1 = 1.99

Non-American Student sample

Number of non-American students in the random sample : sample size : n2 = 12

Sample mean height of non-American students : = 63.3

Sample standard deviation of height of non-American students : s2 = 2.63

Confidence level = 90%

Formula for Confidence Interval for Difference in two Population means when population variances assumed equal

Margin of Error : E

for 90% confidence level = (100-90)/100=0.10

/2 = 0.10/2=0.05

n1 + n2 -2 = 17+12-2=27

t/2,n1+n2-2 =t0.05,27 = 1.70329

Margin of error to be used in constructing the confidence interval: E

Margin of error to be used in constructing the confidence interval: E = 1.459471

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90% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students.

90% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students.

(6.040529,8.959471)