Voting Survey In a survey of 1002 people, 70% said that they v...

Question

Voting Survey In a survey of 1002 people, 70% said that they voted in a recent presidential election (based on data from ICR Research Group). Voting records show that 61% of eligible voters actually did vote.

d. Are the survey results consistent with the actual voter turnout of 61%? Why or why not?

d. Are the survey results consistent with the actual voter turnout of 61%? Why or why not?

Accepted Answer

All right, hello, everyone. So, this question says, a transit agency surveyed 800 city residents and found that 55% reported using public transportation daily. Ridership data from the city's Department of Transportation indicates that the true daily usage rate is 50%. At the 95% confidence interval, are the survey results consistent with the actual 50% usage rate? Why or why not? So let's start with the confidence interval, right? At this point, according to the survey, PAT, which is the proportion of people that reported using public transportation, is equal to 55% or 0.55%. So For the confidence interval, we also need to know the critical value for 95% confidence. So, 95% confidence means that alpha is equal to 0.05. So Z of alpha divided by 2 equals Z 0.025. Which equals approximately 1.96. So from this you can find the standard error. The standard error Is equal to the square root of. Phat multiplied by one subtracted by Phat. And divided by n. With n being the sample size. So standard error Is equal to 0.55, multiplied by 1 subtracted by 0.55. And divided by 800. So evaluating this expression. SE equals approximately 0.01759. And now, with the standard error and our critical Z value, you can find the margin of error. So the margin of error or just capital E. Is equal to Z of 0.025. Multiplied by the standard error. So that equals 1.96. Multiplied by 0.01759. And this equals approximately 0.034475. And now you can proceed to find the upper and lower bounds of the confidence interval. Because recall that the confidence interval is Phat added to and subtracted by the margin of error. So in this case, that's 0.55. Added to and subtracted by 0.034475. So The lower bound of the confidence interval comes out to 0.5155. Whereas the upper bound Is 0.5845. Multiplying both values by 100 converts them both into percentages. So, the 95% confidence interval is between 51.55%. And 58.45%. So now, going back to the last part of the question, the true rate, that's 50%. Is actually below the lower bound of the confidence interval. So now this leads us to our final answer, which is meant to address whether or not the survey results are consistent with the actual usage rate of 50%. The answer, ultimately is no. 50% falls below the lower limit of the 95% confidence interval, indicating the survey overestimates usage. And there you have it. So with that being said, thank you so very much for watching and I hope you found this helpful.

Voting Survey In a survey of 1002 people, 70% said that they voted in a recent presidential election (based on data from ICR Research Group). Voting records show that 61% of eligible voters actually did vote.

d. Are the survey results consistent with the actual voter turnout of 61%? Why or why not?

Key Concepts

Survey Sampling

Response Bias

Statistical Consistency

Watch next

Voting Survey In a survey of 1002 people, 70% said that they voted in a recent presidential election (based on data from ICR Research Group). Voting records show that 61% of eligible voters actually did vote.d. Are the survey results consistent with the actual voter turnout of 61%? Why or why not?

Key Concepts

Survey Sampling

Response Bias

Statistical Consistency

Watch next