The mean annual income of certified welders is normally distributed with a mean

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 0.10, what is the decision rule?

Do not reject the null hypothesis if computed z lies between -1.645 and +1.645; otherwise, reject it. Do not reject the null hypothesis if computed z is greater than 1.645; otherwise, reject it. Do not reject the null hypothesis if computed z lies between -1.960 and +1.960; otherwise, reject it. Reject the null hypothesis if computed z is below -1.960; otherwise, reject it.

Explanation / Answer

It is a two-tailed test.

Given a=0.1, the critical values are Z(0.05) = -1.645 or 1.645 (from standard normal table)

Answer: Do not reject the null hypothesis if computed z lies between -1.645 and +1.645; otherwise, reject it.

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