Question

**Elderly drivers.** A polling agency interviews
866 American adults and finds that 546 think licensed drivers
should be required to retake their road test once they reach 65
years of age. Round all answers to 4 decimal places.

1. Calculate the point estimate for the proportion of American adults that think licensed drivers should be required to retake their road test once they reach 65 years of age.

2. Calculate the standard error for the point estimate you calculated in part 1.

3. Calculate the margin of error for a 95% confidence interval for the proportion of American adults that think licensed drivers should be required to retake their road test once they reach 65 years of age.

4. What are the lower and upper limits for the 95% confidence interval.

( , )

5. Based on a 95% confidence interval, does the poll provide
convincing evidence that *more* than 70% of the population
think that licensed drivers should be required to retake their road
test once they turn 65?

**A.** No, because our confidence interval includes
70%.

**B.** Yes, because a wider confidence interval would
include 70%.

**C.** No, because the plausible values for this
percentage are all less than 70%.

**D.** Yes, because 70% is more than the values in our
confidence interval.

6. Use the information from the polling agency to determine the sample size needed to construct a 90% confidence interval with a margin of error of no more than 4.1%. For consistency, use the reported sample proportion for the planning value of p* (rounded to 4 decimal places) and round your Z-value to 3 decimal places. Your answer should be an integer.

Answer #1

1) point estimate for the proportion =0.6305

2) standard error for the point estimate =0.0164

3) margin of error =0.0321

4) lower and upper limits for the 95% confidence interval =0.5984 ; 0.6626

5)

**C.** No, because the plausible values for this
percentage are all less than 70%.

6)

here margin of error E = | 0.041 | |

for90% CI crtiical Z = | 1.645 | |

estimated proportion=p= | 0.6305 | |

required sample size n = |
p*(1-p)*(z/E)^{2}= |
376.00 |

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