Question

In a test of hypothesis, the null hypothesis is that the population mean is equal to 90 and the alternative hypothesis is that the population mean is not equal to 90. The test is to be made at the 10% significance level. A sample of 100 elements selected from this population produced a mean of 84 and a standard deviation of 8. What is the value of the observed test statistic, z?

Answer 1

Solution :

Given that ,

$\mu$ = 90  

= 84

T

$\sigma$ = 8

n = 100

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 90

H_a : $\mu$   $\neq$ 90

This is the two tailed test .

Test statistic = z

= (
T
- $\mu$ ) / $\sigma$ / $\sqrt$ n

= ( 84 - 90) / 8 / $\sqrt$ 100

= -7.5

The value of the observed test statistic z = -7.5