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 1111 male applicants results in a SAT scoring mean of 1204with a standard deviation of 3838. A random sample of 1919 female applicants results in a SAT scoring mean of 1105with a standard deviation of 3131. 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 critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Find the standard error

Find the lower and upper endpoint

Answer 1

The statistical software output for this problem is:

Two sample T summary confidence interval:
μ₁ : Mean of Population 1
μ₂ : Mean of Population 2
μ₁ - μ₂ : Difference between two means
(without pooled variances)

98% confidence interval results:

Difference	Sample Diff.	Std. Err.	DF	L. Limit	U. Limit
μ1 - μ2	99	13.485239	17.728339	64.529616	133.47038

Hence,

Critical value = 2.556

Standard error = 13.485

Lower endpoint = 64.530

Upper endpoint = 133.470