Question

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis.
​α = 0.08; H1 is μ ≠ 3.24


a. ±1.75


b. 1.75


c. ±1.41


d. 1.41

Answer 1

Answer:

The critical z value used to test a null hypothesis is ±1.75.

Step-by-step explanation:

We are given that the data has a normal distribution and the number of observations is greater than fifty.

Also, the hypothesis given to us is;

Null Hypothesis, $H_0$ : $\mu$ = 3.24

Alternate Hypothesis, $H_1$ : $\mu\neq$ 3.24

This means that our test is two-tailed because in the alternate hypothesis we are concerned with mean value is less than or greater than 3.24.

Also, level of significance (α) = 0.08

Now, for two-tailed test level of significance becomes =  $\frac{\alpha}{2} =\frac{0.08}{2}$ = 0.04

So, in the z-table the critical value of x at 4% significance level is given as 1.75.

Since, this is two-tailed test so the critical z value used to test a null hypothesis would be ±1.75.