Question

Test the claim that for the population of statistics final exams, the mean score is 73 using alternative hypothesis that the mean score is different from 73. Sample statistics include n=18, x¯¯¯=74, and s=16. Use a significance level of α=0.01. (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 73. B. There is not sufficient evidence to reject the claim that the mean score is equal to 73.

Answer 1

Solution :

= 73

= 74

s =16

n = 18

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :    = 73

H_a :    73

Test statistic = t

= ( - ) / s / n

= (74 -73) / 16 / 18

= 0.265

Test statistic = t =  0.265

The significance level is α = 0.01, and the critical value for a two-tailed test is tc = 2.898

P-value = 0.7941

= 0.01  

P-value  ≥

0.7941 ≥ 0.01

The null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean \μ is different than 73, at the 0.01 significance level.