3. The Federal Bureau of Labor Statistics surveyed 50,000 people and found the unemployment rate to be \(5.8\%\). The margin of error was \(0.2\%\). Construct a confidence interval for the unemployment rate. What is the corresponding confidence level? Please interpret this confidence interval by words and graphs, and the confidence coefficient as well.(10%)

4. Before agreeing to purchase a large order of polyethylene sheaths for a particular type of high pressure oil-filled submarine power cable, a company wants to see conclusive evidence that the true standard deviation of sheath thickness is less than .05 inches.(12%) a. What hypotheses should be tested, and why?

b. In this test, what would be a Type I error?

c. In this test, what would be a Type II error?

5. A beer producer claims that the proportion of its customers who cannot distinguish regular from light beer is at most 12 percent. The producer decides to test this null hypothesis against the alternative that the true proportion is more than 12 percent. The decision rule adopted is to reject the null hypothesis if the sample proportion of who cannot distinguish between the two beers exceeds 15 percent.(12%) a. If a random sample of 100 customers is chosen, what is the probability of a Type I error, using this decision rule?

b. Suppose that the true proportion of customers who cannot distinguish between these flavors is 0.20. If a random sample of 100 customers is selected, what is the probability of a Type II error?

6. Information regarding the starting salaries (in $1000) of samples of students in four different majors is given below.(15%) Majors | | Management | Marketing | Finance | Accounting | | --- | --- | --- | --- | --- | | Sample size | 12 | 10 | 9 | 14 | | Average | 26 | 31 | 22 | 25 | | Sample variance | 10 | 7 | 15 | 9 | a. Formulate the hypotheses to determine whether there is a significant difference in the means of the four populations.

b. Set up the ANOVA table for this problem including the test statistic.

c. What is your conclusion at the \(5\%\) level of significance?

7. Shown below is a portion of the computer output for a regression analysis relating sales ($y$ in millions of dollars) and advertising expenditure ($x$ in thousands of dollars).(12%) | Predictor | Coefficient | Standard Error | | --- | --- | --- | | Constant | 4.00 | 0.800 | | x | 0.12 | 0.045 | ANOVA | | df | SS | | --- | --- | --- | | Regression | 1 | 1400 | | Error | 18 | 3600 | a. What has been the sample size for the above regression analysis?

b. Perform a t test and determine whether or not advertising and sales are related. Let \( \alpha = .05 \).

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