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. p1: proportion of successes for population 1 p2: proportion of successes for population 2 p1 - p2 : Difference in proportions 95% confidence interval results: Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. L. Limit U. Limit p1 - p2 1642 3500 1576 3500 0.018857143 0.011911295 -0.0044885665 0.042202852 1) Does your confidence interval capture 0? What does this indicate about the two samples? 2) 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.
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.
p1: proportion of successes for population 1
p2: proportion of successes for population 2
p1 - p2 : Difference in proportions
95% confidence interval results:
|
Difference |
Count1 |
Total1 |
Count2 |
Total2 |
Sample Diff. |
Std. Err. |
L. Limit |
U. Limit |
|
p1 - p2 |
1642 |
3500 |
1576 |
3500 |
0.018857143 |
0.011911295 |
-0.0044885665 |
0.042202852 |
1) Does your confidence interval capture 0? What does this indicate about the two samples?
2) 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.
3) State whether you reject or do not reject the null hypothesis in part (2) and the reason for your decision in one sentence. State your conclusion in context of the problem in one or two complete sentences.
4) What is a possible confounding variable that might have introduced sampling bias into the results of the survey? Answer in one to two sentences.
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