MATH SOLVE

4 months ago

Q:
# 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 0.01? (Round your answer up to the nearest whole number.)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?

Accepted Solution

A:

Answer:At least 9604 drivers need to be surveyed to be 95% confident that the population proportion is estimated to within 0.01.If confidence level is chosen higher than 95% then minimum sample size requried in the survey increasesStep-by-step explanation:The following formula is used to compute the minimum sample size required to estimate the population proportion within the required margin of error:n≥ p×(1-p) × [tex](\frac{z}{ME} )^2[/tex] where n is the sample sizep is the population proportion who always buckle up before riding in a car (estimated as 0.5 when unknown)z is the corresponding z-score for 95% confidence level (1.96)ME is the margin of error in the estimation (0.01)Then, n≥0.5×0.5 × [tex](\frac{1.96}{0.01} )^2[/tex] ≈ 9604If confidence level is chosen higher than 95% then the z value in the equation would be bigger than 1.96. Therefore minimum sample size requried in the survey increases.