Question

Consider the hypotheses shown below. Given that x overbarequals=106​, σ=27​, n=48​, α=0.05​,

complete parts a and b.

Upper H 0H0​:

muμequals =113

Upper H 1H1​:

muμnot equals ≠113

a. what is the​ z-test statistic?

b. what are the critical​ z-score(s)?

c. Because the test statistic _________________ ________ the null hypothesis.

d. what is the p value?

Answer 1

Solution :

= 113

=106

=27​

n = 48

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :    = 113

H_a :     113

a ) Test statistic = z

= ( - ) / / n

= (106 -113) / 27​ / 48

=

Test statistic = z =  

b ) The significance level is α=0.05, and the critical value for a two-tailed test is z_c​=1.96

c ) it is observed that ∣z∣=1.796 ≤ z_c​=1.96, it is then concluded that the null hypothesis is not rejected

P-value = 0.0725

= 0.05  

P-value ≥

0.0725 ≥ 0.05

Do not reject the null hypothesis .

There is insufficient evidence to suggest that