Question

The admissions officer at a small college compares the scores on the Scholastic Aptitude Test (SAT) for the school's in-state and out-of-state applicants. A random sample of 18 in-state applicants results in a SAT scoring mean of 1150 with a standard deviation of 36. A random sample of 12 out-of-state applicants results in a SAT scoring mean of 1113 with a standard deviation of 54. Using this data, find the 95% confidence interval for the true mean difference between the scoring mean for in-state applicants and out-of-state applicants. Assume that the population variances are not equal and that the two populations are normally distributed.
Find the point estimate that should be used in constructing the confidence interval.

Answer 1

Answer:

37

Step-by-step explanation:

Here, we have two different samples, hence, to obtain the confidence interval, we use the relation for the confidence interval for two sample means ;

(x1 - x2) ± Margin of error

Where, (x1 - x2) = point estimate of the sample mean, this is the difference in mean of the two samples.

From the question ;

x1 = 1150 ; x2 = 1113

Hence, the point estimate is : (1150 - 1113) = 37