Question

Consider the following hypothesis test:

H 0 : μ ≥ 21

H a : μ < 21

A sample of 50 provided a sample mean of 20.4. The population standard deviation is 2.

a) Compute the value of the test statistic.

b) What is the p-value?

c) Using α = 0.05, what is your conclusion?

d) Write the rejection rule using the critical value. What is your conclusion?

Answer 1

$H_0: \mu ≥ 21 \\ H_1: \mu < 21 \\ n = 50 \\ \bar{x} = 20.4 \\ \sigma = 2$

a) Test-statistic

$Z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \\ Z = \frac{20.4 -21}{2 / \sqrt{50}} = -2.121$

b) P-value = P(Z< -2.121)

= 0.0169

c) α=0.05

Since p-value is less than α, we reject the null hypothesis and conclude that $\mu < 21$

d) Left-tailed test

Critical value of Z = -1.645

Since $Z < Z_{critical}$ we reject the null hypothesis and conclude that $\mu < 21$