Question

Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion.

28) Test the claim that for the population of history exams, the mean score is 80. Sample data are summarized as n = 16, x = 84.5, and s = 11.2. Use a significance level of ΅ = 0.01.

Answer 1

Solution :

= 80

=84.5

S =11.2

n = 16

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 80

Ha :     80

Test statistic = t

= ( - ) / S / n

= (84.5-80) /11.2 / 16

= 1.607

Test statistic = t = 1.607

P-value =0.1289

= 0.01  

The significance level is α=0.01, and the critical value for a two-tailed test is tc​=2.947.

P-value ≥

0.1289 ≥ 0.01

Do not reject the null hypothesis .

There is insufficient evidence to suggest that