Question

In order to test hypotheses H 0: μ = 70 ; H a: μ < 70.

A random sample of size 100 is taken . The sample yields  x ¯ = 68 ; s = 8.

Find the test statistic.

Group of answer choices

Answer 1

Solution :

$\mu$= 70

$\bar x$ = 68

s = 8

n = 100

df = n-1 = 100- 1 = 99

This is the left tailed test .

The null and alternative hypothesis is

H0 :  $\mu$ = 70

Ha : $\mu$ < 70

Test statistic = t

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

= (68 - 70) / 8 / $\sqrt$ 100

= -2.5

P (t< -2.5 ) = 0.0070

P-value = 0.0070