Question

(1 point) Test the claim that for the population of statistics final exams, the mean score is 78 using alternative hypothesis that the mean score is different from 78. Sample statistics include n = 23, x = 80, and s = 11. 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 not sufficient evidence to reject the claim that the mean score is equal to 78. B. There is sufficient evidence to reject the claim that the mean score is equal to 78.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 78
Alternative Hypothesis: μ < 78

Rejection Region
This is two tailed test, for α = 0.05 and df = 22
Critical value of t are -2.074 and 2.074.
Hence reject H0 if t < -2.074 or t > 2.074

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (80 - 78)/(11/sqrt(23))
t = 0.872

Test statistic, 0.872
positive critical value 2.074
negative critical value -2.074

conclusion: Option A