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 of18male applicants results in a SAT scoring mean of1068with a standard deviation of49. A random sample of12female applicants results in a SAT scoring mean of1160with a standard deviation of37. Using this data, find the95%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%95% confidence interval. Round your answers to the nearest whole number.