Question

A survey is given to 300 random SCSU students to determine their opinion of being a “Tobacco Free Campus.” Of the 300 students surveyed, 228 were in favor a tobacco free campus.

1. Find a 95% confidence interval for the proportion of all SCSU students in favor of a tobacco free campus.
2. Interpret the interval in part a.
3. Find the error bound of the interval in part a.
4. The Dean claims that at least 70% of all students are in favor of a tobacco free campus. Can you support the Dean’s claim at the 95% confidence level? Justify!

For any Hypothesis Test make sure to state Ho, Ha, Test statistic, p-value, whether you reject Ho, and your conclusion in the words of the claim. For any confidence interval make sure that you interpret the interval in context, in addition to using it for inference.

Answer 1

THE CONFIDENCE INTERVAL

Corresponding statistic is given by

where,

We know,

So, 95% confidence interval for the proportion of SCSU students in favor of a tobacco free campus is (0.71, 0.81).

THE HYPOTHESIS TEST

We have to test for null hypothesis

against the alternative hypothesis

Our test statistics is given by

Here,

Sample size

  [Using R-code '1-pnorm(2.267787)']

Level of significance

We reject our null hypothesis if

Here, we observe that

So, we reject our null hypothesis.

Hence, based on the given data we can conclude that there is significant evidence that at least 70 of all students are in favor of a tobacco free campus.

So, we support Dean's claim.