Question

Test the claim that for the population of statistics final exams, the mean score is 7777 using alternative hypothesis that the mean score is different from 77.77. Sample statistics include n=22, x¯=78, and s=16. Use a significance level of .α=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 77.
B. There is sufficient evidence to reject the claim that the mean score is equal to 77.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 77

H_a :    77

= 78

= 77

s = 16

n = 22

df = n - 1 = 22 - 1 = 21

Test statistic = t

= ( - ) / s / n

= (78 - 77) / 16 / 22

= 0.293

Test statistic = 0.293

= 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2, = t_0.025,21 = 2.080

The positive critical value is 2.080
The negative critical value is -2.080

Test statistic < critical value

Fail to reject the null hypothesis .

There is not sufficient evidence to reject the claim that the mean score is equal to 77 .

Option A)