Question

At a local university, a sample of 49 evening students was selected in order to determine whether the average age of the evening students is significantly different from 21. The average age of the students in the sample was 23 years. The population standard deviation is known to be 3.5 years. Use a 0.05 level of significance (z _0.025= -1.96 and z_0.975 = 1.96). Show all four steps of the hypothesis testing.

In case you have difficulties in writing formulas, you can use words to describe what you are doing. You do not need to show any diagrams. Explanation of the purpose of each step and its output satisfies the requirement.

Answer 1

Solution :

$\mu$= 21

$\bar x$ = 23

$\sigma$ = 3.5

n = 49

This is the two tailed test .

The null and alternative hypothesis is

H0 :  $\mu$ = 21

Ha : $\mu$ $\neq$ 21

$\alpha$ = 0.05  

This two tailed test critical value is Zc = -1.96 and +1.96

Test statistic = z

= ($\bar x$ - $\mu$ ) / $\sigma$ / $\sqrt$ n

= ( 23 - 21) / 3.5 / $\sqrt$ 49

= 4

p(Z > 4) = 1-P (Z < 4) = 0

P-value = 0.0000

$\alpha$ = 0.05  

0 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that