Assignment 4STAT 217-03 DUE: November 1All of the questions here refer to the data collected in class given on the attached page. SHOW ALLWORK. No work, no credit.1. Suppose that the 28 responses from the class are a simple random sample from the population of allcollege students in the state of Montana. Is this a reasonable assumption? Why or why not?The students in STAT217-03 were not randomly chosen from the population of all Montana collegestudents, so they are not a simple random sample. Nonetheless, we will proceed in this assignment withthe assumption that these 28 students are still representative of the population of all students at Montanacolleges.2. Using this data, let us consider whether college students who use alcohol tend to support the use of“medicinal marijuana” more than college students who do not use alcohol (these are questions 5 and 18 onthe questionnaire). - State the hypotheses being tested (Hint: we’re testing a single proportion).Let p1 be the proportion of Montana college students who use alcohol, and let p2 be the proportion of Montana collge students who do not use alcohol. The hypotheses are:H0: p1 – p2 = 0Ha: p1 – p2 > 0- Give the test statistic 212111ˆ1ˆˆˆnnppppz=2.330301 where 2121ˆnnXXp= .7143- Give the p-valuep(p1 – p2 > 0)=p(z > 2.330301) = 0.0099- Make a decision at a significance level of .05REJECT H0 since p-value = 0.0099 < .05- State a conclusion in terms of the problem.There is sufficient evidence to suggest that among college students in Montana who drink alcohol, there is more support for allowing the use of medicinal marijuana than among students who do notdrink alcohol.- Give a 95% confidence interval for the difference in proportions of those in favor medicinal marijuana depending on alcohol use.   22211121ˆ1ˆˆ1ˆ*ˆˆnppnppzpp=(0.0747, 0.895)3. There are many hypotheses that one could test regarding two proportions given the data in class. See for example, question 2 above; 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; and in the example given in class, we determined whether there was sufficient evidence to suggest a smaller proportion of women than men supported the marriage amendment to the Montana Constitution. - Choose three different sets of hypotheses that you would like to test re: two proportions from this data set (other than the three I just listed above). Why do you think that you might find evidence in support of each of your hypotheses? - Of the three sets of hypotheses above, let us test one of them. State the hypotheses which you will test using valid statistical notation.- Give the test statistic- Give the p-value- State a conclusion in terms of the problem.- Give a 95% confidence interval for the difference in proportions that you are interested in.4. (a) Use the data in class to find a 95% confidence interval for the proportion of Montana college students who support recognizing the heritage of Montanan’s opportunity to harvest game and fish.   0.7880434) 0.4262424,(280.607142910.607142996.10.6071429ˆ1ˆ*ˆnppzp(b) Is there evidence to suggest that a majority of college students in Monatan support recognizing the heritage of Montanan’s opportunity to harvest game and fish? Why or why not?No, since the confidence interval from (a) is on either side of .5.(c) Suppose that we wish to construct a confidence interval for the true proportion of all Montanans whosupport recognizing the heritage of Montanan’s opportunity to harvest game and fish, and that we want thisconfidence interval to have a margin of error of .03. Use an estimate of p from 4(a) to determine the size of the random sample of Montanans that we must collect to get such a confidence interval.    1018.1116071429.16071429.03.96.1*1**22 ppmzn. Thus, we ought to take a simple random sample of size n=1019 from the population of all Montanans to get a 95% confidence interval which has a margin of error of