The Transform 66 Outside the Beltway project, scheduled to be completed late 2022, is an expansion of the current highway that will provide new travel choices for drivers and hopefully congestion relief from the Capital Beltway (I-495) to Gainesville for a 22.5 mile stretch. This 22.5 mile stretch of I-66 will go through both Fairfax County and Prince William County. VDOT had team members from the project reach out through a phone survey for a random selection of 3,500 residents from both Fairfax County and Prince William County. One question asked on the survey was "Do you feel that the new I-66 Express Lanes will bring congestion relief?" Of the Fairfax County residents surveyed, 1,642 agreed they thought that the expansion will bring congestion relief while only 1,576 of the Prince William County residents surveyed agreed with the statement.

a) Calculate and label the two sample proportions separately and round the values to four decimal places. Next, calculate the difference between these sample proportions by subtracting (Fairfax County - Prince William County). all of these calculations, label each of them.

b) Check the Central Limit Theorem conditions for a confidence interval for the difference between two proportions. For the large sample condition, check and display that each sample has at least 10 successes and 10 failures.

c) Interpret the 95% confidence interval in context in one sentence. In your interpretation, round the confidence limits to four decimal places.

d) Does your confidence interval capture 0? What does this indicate about the two samples?

e) State the null and alternative hypotheses using correct notation if you were to test to see if there is a difference in the proportions for approval between all residents of Fairfax County and Prince William County. 5

f) Display whether you reject or do not reject the null hypothesis in part (f) and the reason for your decision in one sentence. Show 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.

g) What is a possible confounding variable that might have introduced sampling bias into the results of the survey? Answer in one to two sentences.