V506 Homework Exercise 3100 total pointsInstructions: Complete the following homework exercise independently. Submit via .doc or .docxformat via Canvas.Part I:Problems(1)Significance Test for a Mean.By law, an industrial plant can discharge no more than500 gallons of waste water per hour, on the average, into a neighboring lake. Based on otherinfractions they have noticed, an environmental action group believes this limit is beingexceeded. Monitoring the plan is expensive, and a random sample of four hours is selectedover a period of a week. Software reports(5 points)VariableNo. CasesMeanStDevSE of MeanWASTE41000.0400.0200.0a.Test whether the mean discharge equals 500 gallons per hour against the alternative that thelimit is being exceeded. Find theP-value, and interpret.(2.5 points)b.Explain why the test may be highly approximate or even invalid if the population distributionof discharge is far from normal.(2.5 points)(2)Significance Test for a Proportion.Same-sex marriage was legalized across Canadaby the Civil Marriage Act enacted in 2005. Is this supported by a majority, or a minority, ofthe Canadian population? In an Ipsos Global poll conducted forReuter Newsin May 2013 of1000 Canadians that asked whether legalization should stand or be repealed, 63% supportedlegalization. Letdenote the population proportion of Canadian adults who supportlegalization. For testingH0:= 0.50 againstHa:≠0.50(7.5 points)a.Find the standard error, and interpret.(2.5 points)b.Find the test statistic, and interpret.(2.5 points)c.Fine theP-value, and interpret in context.(2.5 points)(3)Decisions and Types of Errors in Tests.Example 6.4 (page 148 in the 5thedition andpage 151 in the 4thedition) tested a therapy for anorexia, usingHo:= 0 andHa: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.TheP-value was 0.018 (5thedition) or 0.017 (4thedition). If the decision for= 0.05 were inerror, what type of error is it?(2.5 points)c.Suppose instead= 0.01. What decision would you make? If it is in error, what type of erroris it?(2.5 points)(4)Limitations of Significance Tests.A report by the Collaborative on AcademicCareers in Higher Education indicated that there is a notable gap between female and male¿01