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

We reject the null hypothesis.

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}{(\sigma)/(√(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.