Assignment 4STAT 217-03 DUE: Friday, October 28All of the questions here refer to the data given in the in class work #7 on proportions, and available athttp://www.math.montana.edu/~parker/courses/STAT217/inclass7_prop.xls . For these questions, SHOWALL WORK. No work, no credit.1. . Consider whether a smaller proportion of women than men support the marriage amendment to theMontana Constitution. - State the hypotheses being tested.Let p1 be the proportion of Montanan females who support the marriage amendment, and let p2 be the proportion of Montanan males who support the marriage amendment. The hypotheses are:H0: p1 = p2 Ha: p1 < p2 - Give the test statistic 65.21885.141014311~1~ˆˆ2121nnppppz where 4643.28103~2121nnXXp- Give the p-valueP(z < -2.65)=.004- Make a decision at a significance level of .05Since p-value =.004 < .05, then we REJECT H0- State a conclusion in terms of the problem.The evidence suggests that that a smaller proportion of Montanan females than men support the marriage amendment. - Give a 95% confidence interval for the difference in proportions of women and men in favor of the marriage ammendment.       0.1803)- (-0.8197,147143.17143.142149.12149.96.11410143ˆ1ˆˆ1ˆ*ˆˆ22211121nppnppzppThus, we are 90% confident that there are 18% to 82% percent MORE women than men who supportthe marriage amendment .- Use MINITAB to confirm the work that you did above, and attach MINITAB’s output to this assignment. From the data at http://www.math.montana.edu/~parker/courses/STAT217/inclass7_prop.xls copy the columns ‘gender’ and ‘marriage’ into the Worksheet in MINITAB. To do the hypothesis test, click on Stat>Basic Statistics>2 Proportions. Select ‘Samples in One Column:’ and in the ‘Samples’ box enter ‘marriage’. In the ‘Subscript’ box, enter ‘gender’. Hit the ‘Options’ button, specify the correct alternative and check ‘Use pooled estimate of p for test’. Now click OK. To do the confidence interval, click on Stat>Basic Statistics>2 Proportions. Select ‘Samples in One Column:’ and in the ‘Samples’ box enter ‘marriage’. In the ‘Subscript’ box, enter ‘gender’. Hit the ‘Options’ button, specify the ‘not equal to’ alternative and uncheck ‘Use pooled estimate of p for test’. Now click OK.Test and CI for Two Proportions: marriage, genderSuccess = 1gender X N Sample p0 3 14 0.2142861 10 14 0.714286Estimate for p(0) - p(1): -0.595% upper bound for p(0) - p(1): -0.231715Test for p(0) - p(1) = 0 (vs < 0): Z = -2.65 P-Value = 0.004* NOTE * The normal approximation may be inaccurate for small samples.Test and CI for Two Proportions: marriage, genderSuccess = 1gender X N Sample p0 3 14 0.2142861 10 14 0.714286Estimate for p(0) - p(1): -0.595% CI for p(0) - p(1): (-0.819681, -0.180319)Test for p(0) - p(1) = 0 (vs not = 0): Z = -3.07 P-Value = 0.002* NOTE * The normal approximation may be inaccurate for small samples.3. There are many hypotheses that one could test regarding two proportions given the data in class. See for example, question 1 above; and in the in-class work, we tested whether a higher proportion ofthose born in Montana supported cyanide leach mining compared to those born somewhere else. - Choose three different sets of hypotheses that you might like to test using two proportions from this data set (other than the three I just listed above). 1. Supporters of Kerry support medicinal marijuana more than supporters of Bush.2. Males support right to fish and hunt more than females.3. Alcohol users tend not to support the tobacco tax as much as non-tobacco users.- Why do you think that you might find evidence in support of each of these hypotheses? 1. Kerry supporte3rs and medicinal marijuana supporters tend to be more politically liberal.2. Males tend to hunt more than females.3. Alcohol users may be more empathetic to users of another drug. 4. (a) Use the data in class to find a 95% confidence interval for the proportion of Montanans who support recognizing the heritage of Montanan’s opportunity to harvest game and fish. .788) 0.4262,(0.18096071.)0.0923(96.16071.28)28171(281796.12817ˆ1ˆ*ˆnppzpAnd so we are 95% confident that the true proportion of Montanans who support the opportunity to harvest game and fish is between 43% and 79%.(b) Is there evidence to suggest that a majority of Montanans support recognizing the heritage of Montanan’s opportunity to harvest game and fish? Why or why not?Since the 95% confidence interval (43%, 79%) includes 50%, then we can not be 95% confident that a majority of Montanan’s support the heritage of Montanans to harvest game and fish.5. We wish to collect another simple random sample so that we can construct a confidence interval for the true proportion of all Montanans who support term limits for legislators, and we want this confidence interval to have a margin of error of .03. Use an estimate of p from the data to determine how large this simple random sample ought to be.For a 95% CI, we will use z* = 1.96. The margin of error m=.03. The estimate for p , is p*=6/28=.2143. Thus,  7.718)2143.1)(2143(.)03.96.1(*1**22 ppmznSo we need a sample of size