Question

Suppose you are testing The sample is large (n = 71) and the variance, σ2, is known. H0:μ=20 vs H1:μ>20. (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 in the question:

Sample size, n = 71

Alpha, α = 0.08

Population variance is known.

First, we design the null and the alternate hypothesis

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

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

Formula:

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

a) We calculate the z-critical with the help of z-table.

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

b)

$z_{stat} = 1.56$

Since,  

$z_{stat} > z_{critical}$

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