Question

Answer only questions 1,2,3,4

The Graduate Management Admission Test (GMAT) is a test required for admission into many masters of business administration (MBA) programs. Total scores on the GMAT are normally distributed and historically have a population standard deviation of 113. The Graduate Management Admission Council (GMAC), who administers the test, claims that the mean total score is 529.

Suppose a random sample of 8 students took the test, and their scores are given below.

699

560

514

570

521

663

727

513

1. Find a point estimate of the population mean.

2. Construct a 95% confidence interval (C.I.) for the true mean score for the population.

3. Does this interval contain the value reported by GMAC?

4. Now use this same sample to construct a 99% C.I. What is it? How does it compare to the 95% C.I.?
5. How many students should be surveyed to estimate the mean score within 25 points with 98% confidence?
6. How many students should be surveyed to estimate the mean score within 25 points with 90% confidence?
7. Compare your answers from questions 5 and 6. What effect does decreasing the confidence level have on the sample size required?

Answer 1

1) The point estimate of the population mean is = (699 + 560 + 514 + 570 + 521 + 663 + 727 + 513)/8 = 595.875

2) At 95% confidence interval the critical value is z_0.025 = 1.96

+/- z_0.025 *

= 595.875 +/- 1.96 * 113/

= 595.875 +/- 78.305

= 517.57, 674.18

3) Yes, the interval contains the value 529 which is reported by GMAC .

4) At 99% confidence interval the critical value is z_0.005 = 2.58

+/- z_0.005 *

= 595.875 +/- 2.58 * 113/

= 595.875 +/- 103.075

= 492.8, 698.95

the 99% confidence interval is more wider than the 95% confidence interval.