Assignment 4STAT 217-03 DUE: Wed, March 22All 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. (4 pts) Consider whether there is a smaller proportion of women than men who support recognizing theheritage of Montanan’s opportunity to harvest game and fish.- State the hypotheses being tested.Let p1 be the proportion of Montanan females who support the heritage to harvest game and fish and let p2 be the proportion of Montanan males who support the heritage to harvest game and fish. The hypotheses are:H0: p1 = p2 Ha: p1 < p2 - Give the test statistic 9348.11846.141114611~1~ˆˆ2121nnppppz where 6071.28116~2121nnXXp- Give the p-valueP(z < -1.9348)=.0268- Make a decision at a significance level of .05Since p-value =.0268 < .05, then we REJECT H0- State a conclusion in terms of the problem.The evidence suggests that a smaller proportion of Montanan females than men support the heritage to harvest game and fish. - Give a 95% confidence interval for the difference in proportions of women and men in favor of the hunting and fishing amendment.       0.0204)- (-0.6939147857.17857.144286.14286.96.11411146ˆ1ˆˆ1ˆ*ˆˆ22211121nppnppzppThus, we are 95% confident that there are 2% to 69% MORE men than women who support the heritage to harvest game and fish. 2. (1 pt) MINITAB output. If you provided no output, -5 pts.3. (2 pts) 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 of those 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 supporters 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. (2 pts) (a) Find a 95% confidence interval for the proportion of Montanans who support cyanide leach mining. 0.4944) , 0.1484()0.0883(96.13214.28)2891(28996.1289ˆ1ˆ*ˆnppzp. And so we are 95% confident that the true proportion of Montanans who support cyanide leach mining is between 15% and 49%.(b) Is there evidence to suggest that a majority of Montanans support cyanide leach mining? Why or why not?Since the 95% confidence interval (15%, 49%) is below 50%, then we are 95% confident that a MINORITY of Montanan’s support cyanide leach mining.5. (1 pt) We wish to collect another simple random sample so that we can construct a 95% 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 howlarge 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