Question

What is the average age of students who live off campus? A random sample of 51 students shows the mean of 21.7 years and the standard deviation 2.5 years. Use a 95% level of confidence.

a. What is the population parameter to estimate?

b. What is the sample statistic?

c. Find a 95% confidence interval for population parameter.

d. Interpret your interval in the context.

e. Melinda assumes that students who live off campus, on average, are older than 25. Is she correct?

Answer 1

Given that sample size n = 51 sample mean 1 = 21.7 years, Sample standard deviation S = 2.5 years a) The population parameter to estimate is Population mean, 4 (Estimate) b) The sample statisticis sample mean 7 = 21.7 years ន S c)95% Confidence iterval is 1-2 2 * + ZahJn) % at = X-2 Where a = 5% = 0.05, 2a =1.96 (From 2-tables) Where Sis sample standard deviation S ន 2.5 2.5 +z 7-(1.96) 21.7+(1.96) 151 151, - (21.7 -0.6861, 21.7+0.6861) = (21.0139, 22.3861) 95% Confidence iteral is (21.0139, 22.3861) d)The population mean fal in the interval (21.0139, 22.3861) has 95% confidence. ie P(21.0139<u<22.3861) = 0.95 e) No. She is not correct since the confidence interval is (21.0139, 22.3861) which not include 25. Hence Melinda is not correct.