Question

Consider the hypotheses shown below. Given that x =105​, σ = 26​, n = 45​, α = 0.01​,

complete parts a and b.

Upper H0​: μ = 113

Upper H1​: μ ≠113

​a) What conclusion should be​ drawn?

​b) Determine the​ p-value for this test.

Answer 1

Solution :

= 113

=105

=26

n = 45

this is the two tailed test .  

The null and alternative hypothesis is ,

H0 :   = 113

Ha :     113

Test statistic = z

= ( - ) / / n

= (105-113) / 26/ 45

= -2.06

P(z < -2.06 ) = 0.0197

P-value = 2*0.0197=0.0394

a)

= 0.01

P-value >

do not Reject the null hypothesis .

There is sufficient evidence to suggest that   

Using the P-value approach: The p-value is p = 0.039p=0.039, and since p = 0.039 \ge 0.01p=0.039≥0.01, it is concluded that the null hypothesis is not rejected.

b) p value =0.0394