(1)Significance Test for a Mean. By law, an industrial plant can discharge no more than 500 gallons of waste water per hour, on the average, into a neighboring lake. Based on other infractions they have noticed, an environmental action group believes this limit is being exceeded. Monitoring the plan is expensive, and a random sample of four hours is selected over a period of a week. Software reports (5 points)

VariableNo. CasesMeanStDevSE of Mean

WASTE41000.0400.0200.0

a.Test whether the mean discharge equals 500 gallons per hour against the alternative that the limit is being exceeded. Find the P-value, and interpret. (2.5 points)

b.Explain why the test may be highly approximate or even invalid if the population distribution of discharge is far from normal. (2.5 points)

(2)Significance Test for a Proportion. Same-sex marriage was legalized across Canada by the Civil Marriage Act enacted in 2005. Is this supported by a majority, or a minority, of the Canadian population? In an Ipsos Global poll conducted for Reuter News in May 2013 of 1000 Canadians that asked whether legalization should stand or be repealed, 63% supported legalization. Let p denote the population proportion of Canadian adults who support legalization. For testing H₀: m = 0.50 against H_a: m 0.50 (7.5 points)- stored in pdf anser

a.Find the standard error, and interpret. (2.5 points)

b.Find the test statistic, and interpret. (2.5 points)

c.Fine the P-value, and interpret in context. (2.5 points)

(3)Decisions and Types of Errors in Tests. Example 6.4 (page 148 in the 5^th edition and page 151 in the 4^th edition) tested a therapy for anorexia, using H_o: m = 0 and H_a: m 0 about the population mean weight change. (7.5 total points)

a.In the words of that example, what is (i) Type I error? (ii) Type II error? (2.5 points)

b.The P-value was 0.018 (5^th edition) or 0.017 (4^th edition). If the decision for a = 0.05 were in error, what type of error is it? (2.5 points)

c.Suppose instead a = 0.01. What decision would you make? If it is in error, what type of error is it? (2.5 points)

(4)Limitations of Significance Tests. A report by the Collaborative on Academic Careers in Higher Education indicated that there is a notable gap between female and male academics in their confidence that tenure rules are clear, with men feeling more confident. The 4500 faculty members in the survey were asked to evaluate policies on a scale of 1 to 5 (very unclear to very clear). The mean response about the criteria for tenure was 3.51 for females and 3.55 for males, which was indicated to meet the test for statistical significance. Use this study to explain the distinction between statistical significance and practical (or economic) significance. In other words, even if a difference is statistically significant, is the magnitude of the difference important from a practical policy standpoint? (5 total points)