select the correct answer.\nthe city transit authority surveyed 1,000 citizens who regularly use public…

select the correct answer.\nthe city transit authority surveyed 1,000 citizens who regularly use public transportation. of those surveyed, 658 users said they paid using a monthly subscription as opposed to paying for each ride individually. the transit authoritys report claims, we can be 95% confident that the percentage of citizens using public transportation with a monthly subscription is between 63.33% and 68.27%.\nwhich statement best describes this claim?\n\na. the reports claim is false because the margin of error is 3.87%.\nb. the reports claim is false because the margin of error is 2.94%.\nc. the reports claim is true.\nd. there is not enough information to evaluate the reports claim.

select the correct answer.\nthe city transit authority surveyed 1,000 citizens who regularly use public transportation. of those surveyed, 658 users said they paid using a monthly subscription as opposed to paying for each ride individually. the transit authoritys report claims, we can be 95% confident that the percentage of citizens using public transportation with a monthly subscription is between 63.33% and 68.27%.\nwhich statement best describes this claim?\n\na. the reports claim is false because the margin of error is 3.87%.\nb. the reports claim is false because the margin of error is 2.94%.\nc. the reports claim is true.\nd. there is not enough information to evaluate the reports claim.

Answer

Explanation:

Step1: Calculate the sample proportion

The sample proportion $\hat{p}=\frac{658}{1000} = 0.658$

Step2: Calculate the margin of error for a 95% confidence interval

For a large - sample proportion confidence interval, the margin of error $E$ for a 95% confidence interval is calculated using the formula $E = z\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$, where $z\approx1.96$ for a 95% confidence interval, $\hat{p}=0.658$, and $n = 1000$.

First, calculate $\hat{p}(1 - \hat{p})=0.658\times(1 - 0.658)=0.658\times0.342 = 0.225036$

Then, $\frac{\hat{p}(1 - \hat{p})}{n}=\frac{0.225036}{1000}=0.000225036$

$\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}=\sqrt{0.000225036}\approx0.015$

$E = 1.96\times0.015=0.0294 = 2.94%$

The confidence interval is $\hat{p}\pm E=0.658\pm0.0294=(0.6286,0.6874)$ or $(62.86%,68.74%)$

The given confidence interval in the report is $(63.33%,68.27%)$ which is within the calculated confidence - interval range.

Answer:

C. The report's claim is true.