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 15 male applicants results in a SAT scoring mean of 1151 with a standard deviation of 37. A random sample of 6 female applicants results in a SAT scoring mean of 1095 with a standard deviation of 38. Using this data, find the 95% 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 critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 2 of 3:Find the standard error of the sampling distribution to be used in constructing the confidence interval. Round your answer to the nearest whole number.

Step 3 of 3:Construct the 95% confidence interval. Round your answers to the nearest whole number.

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 15 male applicants results in a SAT scoring mean of 1151 with a standard deviation of 37. A random sample of 6 female applicants results in a SAT scoring mean of 1095 with a standard deviation of 38. Using this data, find the 95 % 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 critical value that should be used in constructing the confidence interval. Round your answer to three decimal places. > Next Keypad 2 Points Answer(How to Enter)

Answer 1

The statistical software output for this problem is:

Two sample T summary confidence interval: Vi : Mean of Population 1 12 : Mean of Population 2 V1-2Difference between two means (without pooled variances) 95% confidence interval results: Difference Sample Diff. Std. Err. DF L. Limit U. Limit Vi - P2 56 18.219038 9.0466532 14.81805 97.18195

Hence,

Step - 1: Critical value = 2.260

Step - 2: Standard error = 18

Step - 3: Lower endpoint = 15

Upper endpoint = 97