Question

1. You administered a survey to a sample of 401 high school sophomores and found a mean narcissism score of 91.3 with a standard deviation of 10. However, a recent study of high school seniors found that the average narcissism score was 92.

Based on this prior research, test the null hypothesis that your sample of high school sophomores came from a population of high school sophomores in which the mean narcissism score is 92 against the alternative hypothesis that your sample was drawn from a population with a mean narcissism score that is less than 92. Use alpha = .05

a) For this problem, what is the population you are trying to learn about?

b) Formally state the null and the alternative hypothesis for this test ?

c) What is the critical value(s) for this test ?

d) Compute and report the test statistic (i.e., the z or t score).

e) Interpret your decision regarding the null hypothesis.

f) If necessary, compute 95% confidence intervals for the population mean and interpret them.

Answer 1

(a) Population : High school sophomores (6) Let u = true population mean narcissism score. Null hypothesis, Ho :=92 vs. Alternative hypothesis, HA:N < 92 (c) Critical value = -10.05.400 = -1.6487 (d) t-score = Vnt -92) - = -1.4017 S where, n = 401, T = sample mean = 91.3, s = sample sd = 10 (e) Since Value of t-score > Critical value so we fail to reject null hypothesis at 5% level of significance and conclude that the sample of high school sophomores came from a population of high school sophomores. of higfonclude that the's fail to reject nulla (f) 95% CI for u is S ( 7 – to.25,00 x tapa 1 + $0.025,400 x ) = (90.32, 92.28) where, to.025,400 = 1.9659 We are 95% confident that true population mean narcissism score lies within (90.32, 92.28).

Since 92 lies in this interval so we are 95% confident that the sample of high school sophomores came from a population of high school sophomores in which the mean narcissism score is 92.