Question

3. Suppose you are testing H0 : µ = 20 vs H1 : µ > 20. The sample is large (n = 71) and the variance, σ 2 , is known. (a) Find the critical value(s) corresponding to α = 0.08. (b) You find that z = 1.56. Based on your critical value, what decision do you make regarding the null hypothesis (i.e. do you Reject H0 or Do Not Reject H0)?

Answer 1

Answer:

We reject the null hypothesis.

Step-by-step explanation:

We are given the following information in the question:

Sample size, n = 71

Population variance is known.

Level of significance, α = 0.08

$z_{\text{stat}} = 1.56$

The null and alternate hypothesis are:

$H_{0}: \mu = 20\\H_A: \mu > 20$

We use one-tailed z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} } = 1.56$

Now, $z_{critical} \text{ at 0.08 level of significance } = 1.41$

Since,  

$z_{stat} > z_{critical}$

We fail to accept the null hypothesis and reject it and accept the alternate hypothesis.