Question

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

• Part (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 0.04? (Round your answer up to the nearest whole number.)
  

Answer 1

Solution:

Given,

E = 0.04

c = 95% = 0.95

Now,

= 1 - c = 1 - 0.95 = 0.05

/2 = 0.025

= 1.96 (using z table)

No prior information of p is available.

In this case ,

take p = 0.5

1 - p = 1 - 0.5 = 0.5

The sample size for estimating the proportion is given by

n =

= (1.96)² * 0.5 * 0.5 / (0.04²)

= 600.25

= 601 ..(round to the next whole number)

Answer : n = 601