Question

GMU officials are trying to determine if they are using the correct number of campus shuttles for the number of students who use them. If the proportion of students who use the shuttles is significantly different from 0.28, the officials believe they will have to either remove or add a shuttle to the fleet. In a random sample of 444 people taken from the population of all individuals associated with GMU (including faculty, staff, and students) it was discovered that 123 of these individuals use the shuttle.

1. Check the three conditions of the Central Limit Theorem that allow you to use the one-proportion confidence interval using one complete sentence for each condition. Show work for the numerical calculation.

2. Construct a 99% confidence interval to estimate the population proportion of these individuals who use the shuttle system. Calculate this “by hand” using the formula and showing your work (please type your work, no images accepted here). Round your confidence limits to four decimals.

4. Using a = 0.01, is there sufficient evidence to conclude that the proportion of students who use GMU shuttles is different from 0.28? Conduct a full hypothesis test by following the steps below. Enter an answer for each of these steps in your document.

1. Define the population parameter in one sentence.
2. State the null and alternative hypotheses using correct notation.
3. State the significance level for this problem.
4. Calculate the test statistic “by-hand.” Show the work necessary to obtain the value by typing your work and provide the resulting test statistic. Do not round during the calculation. Then, round the test statistic to two decimal places after you complete the calculation.
5. Calculate the p-value using the standard Normal table and provide the answer. Use four decimal places for the p-value.
6. State whether you reject or do not reject the null hypothesis and the reason for your decision in one sentence (compare your p-value to the significance level to do this).
7. State your conclusion in context of the problem (i.e. interpret your results and/or answer the question being posed) in one or two complete sentences.
8. Use StatCrunch (Stat à Proportion Stats à One Sample à with Summary) to verify your test statistic and p-value. Copy and paste this box into your document.

5. Explain the connection between the confidence interval and the hypothesis test in this problem (discuss this in relation to the decision made from your hypothesis test and connect it to the confidence interval you constructed in part (b)). Answer this question in one to two sentences.

PLEASE LETTER /NUMBER UR ANSWER

Answer 1