Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

imagine that students at Abraham Page 47 STUDENT NAME DATE TAKE IT HOME 1 Imagin

ID: 3315601 • Letter: I

Question

imagine that students at Abraham Page 47 STUDENT NAME DATE TAKE IT HOME 1 Imagine that students at Abraham Lincoln High School take an achievement test before they apply to colleges. A researcher who is interested in the students' college placement wishes to estimate the mean score of all students at the school who take the achievement test. The researcher selects a simple random sample of 15 students from the school. For this sample, -525 and s 24. Assume that the test scores are normally distributed. Construct a 99% confidence interval for , which is the population mean score for Abraham Lincoln High School. A Are the criteria for approximate normality satisfied? Explain. B Determine the sample mean, sample standard deviation, and sample size. C Determine the critical value that corresponds to the 99% confidence level. D Compute the margin of error (E) for a 99% confidence interval. E Construct a 99% confidence interval

Explanation / Answer

1.

Yes the normality criteria is satisfied as sample is taken from normally distributed population and sample size is greater than 5.

B.

sample size = 15

sample mean = 525

sample std. dev. = 24

C. Critical value is

z-value of 99% CI 2.5758

D.

SE = std.dev./sqrt(n) = 6.19677

Margin of error = ME = z*SE = 15.9618

E.

Lower Limit = Mean - ME 509.03817

Upper Limit = Mean + ME 540.96183

99% CI = (509.0382 , 540.9618 )

2.

Yes the normality criteria is satisfied as sample is taken from normally distributed population and sample size is greater than 5.

CI for 99% n 15 mean 525 z-value of 99% CI 2.5758 std. dev. 24 SE = std.dev./sqrt(n) 6.19677 ME = z*SE 15.96183 Lower Limit = Mean - ME 509.03817 Upper Limit = Mean + ME 540.96183 99% CI (509.0382 , 540.9618 )