Shelly polled students at her university to see what proportion are in favour of a slight tuition increase to fund construction of the new student union building. She took a simple random sample of 250 students. In her sample, 131 were in favour of the tuition increase. (PLEASE answer all questions as they're short and connected/based off of each other!) (a) Suppose Shelly were to (hypothetically) repeat this process many times, taking a simple random sample of 250 students each time. If 50% of all students at the university were in favour of the tuition increase, what would be the approximate sampling distribution of Shelly’s sample proportions? Show your work. (b) Using Shelly’s data, calculate a 90% confidence interval for the proportion of students at the university who are in favour of the tuition increase. (You can do this either by hand or using R, but remember to show all your work.) (c) How large of a sample size would Shelly need, if she wanted to construct a 90% confidence interval that had a margin of error of 0.02? Show your work.
Shelly polled students at her university to see what proportion are in favour of a slight tuition increase to fund construction of the new student union building. She took a simple random sample of 250 students. In her sample, 131 were in favour of the tuition increase.
(PLEASE answer all questions as they're short and connected/based off of each other!)
(a) Suppose Shelly were to (hypothetically) repeat this process many times, taking a simple random sample of 250 students each time. If 50% of all students at the university were in favour of the tuition increase, what would be the approximate sampling distribution of Shelly’s sample proportions? Show your work.
(b) Using Shelly’s data, calculate a 90% confidence interval for the proportion of students at the university who are in favour of the tuition increase. (You can do this either by hand or using R, but remember to show all your work.)
(c) How large of a
(d) Shelly believes that more than half of the students at the university are in favour of the tuition increase. State the null and alternative hypotheses for testing this claim. Be sure to define in words the meaning of the parameter “p,” in the context of this problem.
(e) Carry out a test of significance on the hypotheses in part (d). Show your work at each step. (You can complete the calculations either by hand or using R, but remember to show all your work.)
(f) Was your result in part (e) statistically significant, or not statistically significant?
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