The admissions officer at a small college compares the scores on the Scholastic
ID: 3359103 • Letter: T
Question
The admissions officer at a small college compares the scores on the Scholastic Aptitude Test (SAT) for the school's male and female applicants. A random sample of 9 male applicants results in a SAT scoring mean of 1081 with a standard deviation of 51. A random sample of 14 female applicants results in a SAT scoring mean of 1049 with a standard deviation of 55. Using this data, find the 98% confidence interval for the true mean difference between the scoring mean for male applicants and female applicants. Assume that the population variances are not 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 98% confidence interval. Round your answers to the nearest whole number.
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
(without pooled variances)
98% confidence interval results:
Hence,
1) Point estimate = 32
2) Margin of error = (89.306802 - (-25.306802))/2 = 57.306802
3) 98% confidence interval: (-25, 89)
Difference Sample Diff. Std. Err. DF L. Limit U. Limit 1 - 2 32 22.473794 18.18042 -25.306802 89.306802Related Questions
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