Question

We are given that n=15, the sample mean Ῡ=2.5, the sample standard deviation s=1.5 and random variable Y distributed Normal with mean µ and variance σ², where both µ and σ² are unknown and we are being concentrated on testing the following set of hypothesis about the mean parameter of the population of interest.

We are to test:

H₀ : µ ≥ 3.0 versus H₁ : µ < 3.0.

Compute the following:

a) P- value of the test

b)    Probability of making Type II error and the power of this test at µ= 2.0

Answer 1

a) Test for single mean:

Test Statistic:

The p-value is p = 0.1088

b) P(type II erro) and Power test calculations: