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 = 0.1 for a two-tailed test. a. ±1.645b. ±2.052c. ±1.4805d. ±2.33

According to the z-distribution, the critical value is given by:

a. ±1.645

The critical value for a two-tailed test with a significance level of is |z| such that -z has a p-value of .

In this problem, , then .

A similar problem is given at link

The critical z value used to test a null hypothesis is ±1.645.

Step-by-step explanation:

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

And we have to find the critical z value used to test a null hypothesis at α = 0.1 for a two-tailed test.

Firstly, as we know that to find the critical z value we need only the level of significance to be known.

Here, the level of significance is given = = 0.10

But for the two-tailed test, the level of significance to be considered is given by = = = 0.05 or 5%.

Now, in the z table; we can see that the critical z value at a 5% level of significance (for the two-tailed test) is given as 1.645.

Hence, the critical z value used to test a null hypothesis at α = 0.1 for a two-tailed test is ±1.645.