Question

Test H0: μ ≤ 8 versus HA: μ > 8, given α = 0.01, n = 25, X = 8.13 and s = 0.3. Assume the sample is selected from a normally distributed population.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 8

H_a : > 8

Test statistic = t

= ( - ) / s / n

= (8.13 - 8) / 0.3 / 25

= 2.17

P(z > 2.17) = 1 - P(z < 2.17) = 0.015

P-value = 0.015

= 0.01

P-value >

Fail to reject the null hypothesis .