Question

According to the U.S. Bureau of Labor Statistics, the average weekly earnings of a production worker in July 2011 were $657.49. Suppose a labor researcher wants to test to determine whether this figure is still accurate today. The researcher randomly selects 54 production workers from across the United States and obtains a representative earnings statement for one week from each. The resulting sample average is $672.41. Assuming a population standard deviation of $63.90 and a 5% level of significance, determine whether the mean weekly earnings of a production worker have changed.

(Round your answer to 2 decimal places.)

The value of the test statistic is and we

fail to reject the null hypothesis or

reject the null hypothesis

.

Answer 1

As we are testing here whether the mean weekly earnings of a production worker have changed, therefore the null and the alternative hypothesis here are given as:

The test statistic here is computed as:

As this is a two tailed test, the p-value here is computed from the standard normal tables here as:

p = 2P( Z > 1.7158) = 2*0.0431 = 0.0862

As the p-value here is 0.0862 > 0.05 which is the level of significance, therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence here that the mean has changed from the previous value.