The admissions officer at a small college compares the scores on the Scholastic

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 8 male applicants results in a SAT scoring mean of 1134 with a standard deviation of 26. A random sample of 17 female applicants results in a SAT scoring mean of 1173 with a standard deviation of 40. Using this data, find the 80%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 80% confidence interval. Round your answers to the nearest whole number.

Lower endpoint is________and Upper endpoint is__________

Explanation / Answer

Ans:

1)n1=8,n2=17

critical t values for 80% CI and df=8-1=7

(we consider df as smaller of n1-1 or n2-1 in unequal population variances)

(significance level=1-0.8=0.2)

critical t value(two tailed)=TINV(0.2,7)=+/-1.415

2)

standard error=sqrt((26^2/8)+(40^2/17))=13.36

standard error=13

3)

80% Confidence interval

=(1134-1173)+/-1.415*13

=-39+/-18.40

=(-57.4,-20.6)

=(-57,-21)

lower endpoint=-57

upper endpoint=-21

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