Question

Previous Problem Problem List Next Problem (4 points) Test the claim that for the population of statistics final exams, the mean score is 75 using alternative hypothesis that the mean score is different from 75. Sample statistics include n = 23, x = 76, and s = 12. Use a significance level of a = 0.05. (Assume normally distributed population.) The test statistic is The positive critical value is The negative critical value is The conclusion is A. There is sufficient evidence to reject the claim that the mean score is equal to 75. B. There is not sufficient evidence to reject the claim that the mean score is equal to 75.

Answer 1

Solution: Given that n = 23, x = 76, s = 12, α = 0.05
df = n-1 = 23-1 = 22

The null and alternative hypothesis :
H0 : μ = 75
H1 : μ not = 75

The test statistic is 0.3997
= t = (X-μ)/(s/sqrt(n))
= (76-75)/(12/sqrt(23))
= 0.3997

The positive critical value is 2.074

The negative critical value is -2.074

=> option B.