**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.

**2. Variable gas production**

The data for this assignment are listed in the Excel file *Variable gas production*.

With gasoline prices increasing, drivers are more concerned with their cars’ gasoline consumption. For the past 5 years, a driver has tracked the gas mileage of his car and found that the standard deviation from fill-up to fill-up was miles per gallon. Now that his car is 5 years old, he would like to know whether the variability of gas mileage has changed. He recorded the gas mileage from his last eight fill-ups; these are listed in the data files.**a.** Formulate the null hypothesis and the alternative hypothesis .**b.** Which test statistic should be used?**c.** Infer at a 10% significance level whether the variability has changed. Explain your answer.

**Solution.****a.** .**b.** The test statistic is .**c.** This is a two-sided test and thus the rejection region is: .

From the data in the data file we compute (by Excel). Thus, the test statistic is . This number is not in the rejection region, so there is not enough evidence to infer that the population variance has changed.