Question

In a test of the hypothesis H0: μ=10 versus Ha: μ≠10 a sample of =50 observations possessed mean overbar x=10.6 and standard deviation s=2.6 Find and interpret the​ p-value for this test

The​ p-value for this test is __________. (Round to four decimal places as​ needed.)

Interpret the result. Choose the correct answer below.

A. There is sufficient evidence to reject H0 for α > 0.11.

B.There is insufficient evidence to reject H0 for α=0.15.

C.There is sufficient evidence to reject H0 for α < 0.11.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 10

H_a : $\mu$   $\neq$ 10

$\bar x$ = 10.6

$\mu$ = 10

s = 2.6

n = 50

Test statistic = t

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

= (10.6 - 10) / 2.6 / $\sqrt$ 50

= 1.63

Test statistic = 1.63

Degrees of freedom = n - 1 = 50 - 1 = 49

P-value = 0.1095

The​ p-value for this test is 0.1095 .

$\alpha$ = 0.11

P-value < $\alpha$

Reject the null hypothesis .

C.There is sufficient evidence to reject H ₀ for α < 0.11.