Return to Assignments Hypothesis testing (one population)

**1. Company blue-collar workers**

The data for this assignment are listed in the Excel file *Company blue-collar workers*.

In the midst of labor-management negotiations, the president of a company argues that the company’s blue-collar workers, who are paid an average of 30000 dollars per year, are well-paid because the mean annual income of all blue-collar workers in the country is less than 30000 dollars. That figure is disputed by the union, which does not believe that the mean blue-collar income is less than 30000 dollars. To test the company president’s belief, an arbitrator draws a random sample of 350 blue-collar workers from across the country and asks each to report his or her annual income. The arbitrator assumes that the blue-collar incomes are normally distributed with a standard deviation of 8000 dollars.**a.** Compute the mean blue-collar annual income of the sample.**b.** What would you take as null hypothesis and alternative hypothesis ?**c.** What is the test statistic and can it be inferred at the 5% significance level that the company president is correct? Explain your answer.**d.** What test statistic would you use if the population standard deviation of the blue-collar incomes is not known? Explain the consequences.

**Solution.****a.** The mean blue-collar income can be computed using Excel: 29120 dollars.**b.** **c.** The test statistic is:

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This is a one-sided test and thus the rejection region is , so there is not enough evidence to infer that the null hypothesis is correct. We may infer that the president is right. One could also compute the -value which is which is much less than the significance level 0.05.**d.** If the population standard deviation would not be known, the sample standard deviation is used. Then the test statistic would be . Instead of the rejection level the rejection level has to be used. Since is large the difference can be neglected.