Question

A sample​ mean, sample​ size, and sample standard deviation are provided below. Use the​ one-mean t-test to perform the required hypothesis test at the 5% significance level.

X=25 s=9 n=24 H0: u=24 Ha: u>24

Answer 1

Solution :

This is the two tailed test,  

The null and alternative hypothesis is ,

H₀ :   = 24

H_a : > 24

Test statistic = t =

= ( - ) / s / n

= (25 - 24 ) / 9 / 24

Test statistic = t = 0.54

degrees of freedom = n - 1 = 24 - 1 = 23

P(t > 0.54 ) = 1-P (t < 0.54 ) = 1 - 0.7028

P-value = 0.2972

= 0.05  

P-value >

Fail to reject the null hypothesis.