Question

Consider H0 : μ = 72 versus H1 : μ > 72 ∶ A random sample of 16 observations taken from this population produced a sample mean of 75.2. The population is normally distributed with σ = 6.

a. Calculate the p-value.

b. Considering the p-value of part a, would you reject the null hypothesis if the test were made at a significance level of .01?

c. Find the critical value and compare it with the test statistic. What would the conclusion be at a significance level of .01?

Answer 1

Solution :

Given that,

= 75.2

= 72

= 6

n = 16

Test statistic = z = ( - ) / / n

= (75.2 - 72) / 6 / 16 = 2.13

Test statistic = 2.13

This is the right tailed test .

P(z > 2.13) = 1 - P(z < 2.13) = 1 - 0.9834 = 0.0166

(a and b)

P-value = 0.0166

= 0.01

P-value >  

Fail to reject the null hypothesis .

(c)

= 0.01

Z = Z_0.01 = 2.326

crtical value = 2.326

Test statistic < crtiical value

Fail to reject the null hypothesis .