Question 2 UNMC is concerned about students smoking at the campus. From a random sample of 200 students, 22 of them were smokers. (a) Calculate the point estimate of the true proportion of smokers at the campus. [5 marks] (b) Construct a 99\% confidence interval within which the true proportion of smokers will lie. [15 marks]
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- The point estimate for the proportion of smokers is given by the formula: \[ \hat{p} = \frac{x}{n} \] where \( x \) is the number of smokers, and \( n \) is the total number of students sampled. Show more…
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Problem 1. We are interested in estimating the proportion of students at a university who smoke. Out of a random sample of 210 students from this university, 45 students smoke. (a) (5 points) Calculate a 95% confidence interval for the proportion of students at this university who smoke. (Reminder: First check conditions for such a confidence interval to be valid.) (b) (5 points) If we wanted the margin of error to be no larger than 3% at a 95% confidence level for the proportion of students who smoke, how big of a sample would we need?
Clarissa B.
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