Question

Suppose that a car company wants to determine the importance to consumers for service like OnStar, which offers drivers a wifi connection (among other things). Small/preliminary studies have concluded that about 69% of people would like an wifi connection in there car.

A) use the given preliminary estimate to determine the sanple size required to estimate the proportion of adult Americans who would like wifi capablities in their car to within .02 with 95% confidence.

B) how would the interval be affected if 99% confidence interval was desired.

-the interval would get larger

-the intercal would get smaller

-the population proportion would change

C) use the given preliminary estimate to determine the sample size required to estimate the proportion of adult Americans who would like wifi capabilities in their car to within .02 with 99% confidence.

Answer 1

Solution:

Given ,

p = 69% = 0.69

1 - p = 1 - 0.69 = 0.31

A)

E = 0.02

c = 95% = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.025

Using Z table ,

= 1.96

The sample size for estimating the proportion is given by

n =

= (1.96)² * 0.69 * 0.31 / (0.02²)

= 2054.2956

= 2055 ..(round to the next whole number)

Answer : Required Sample size is n = 2055

B) how would the interval be affected if 99% confidence interval was desired.

the interval would get larger

(Because as the confidence level increases , critical value increases and then margin of error increases)

C)

E = 0.02

c = 99% = 0.99

= 1- c = 1- 0.99 = 0.01

  /2 = 0.005

Using Z table ,

= 2.576

The sample size for estimating the proportion is given by

n =

= (2.576)² * 0.69 * 0.31 / (0.02²)

= 3548.481216

= 3549 ..(round to the next whole number)

Answer : Required Sample size is n = 3549