Question

Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car.

a) When designing a study to determine this population proportion, what is the minimum number of drivers you would need to survey to be 95% confident that the population proportion is estimated to within 0.02? (Round your answer up to the nearest whole number.)

_______ drivers

b) If it was later determined that it was important to be more than 95% confident and a new survey was commissioned, how would that affect the minimum number you would need to survey? Why?

If the confidence level is increased, then the sample size would need to increase because a higher level of confidence increases the margin of error.

If the confidence level is increased, then the sample size would need to decrease because we would like the proportion of people who buckle up to be around 50%.

If the confidence level is increased, then the sample size would need to decrease because increasing the sample size would create an even larger interval.

If the confidence level is increased, then the sample size would not be affected.

Answer 1

b) If it was later determined that it was important to be more than 95% confident and a new survey was commissioned, how would that affect the minimum number you would need to survey? Why?

Here we want to be 99% confident or more than 95% confident.

As confidence level increases confidence interval and the margin of error would be increased & confidence interval would get wider.

If the confidence level is increased, then the sample size would need to increase because a higher level of confidence increases the margin of error.