Question

The mean annual income of certified welders is normally distributed with a mean of $50,000 and a population standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. If the level of significance is .10, what is the critical value

Answer 1

Answer: 1.645

Step-by-step explanation:

Given : The mean annual income of certified welders is normally distributed with a mean of $50,000 and a population standard deviation of $2,000.

Alternative hypothesis :
`H_a:\mu\\eq50000`

Since the alternative hypothesis is two-tailed , so the hypothesis test is a two-tailed test.

Also, Significance level :
`\alpha=0.10`

For two tailed test the to find the critical value , we need to find the z value or t-value for significance level of
`\alpha/2`.

The critical value will be:

`z_(0.10/2)=z_(0.05)=1.645`