Question

In spite of the potential safety hazards, some people would like to have an Internet connection in their car. A preliminary survey of adult Americans has estimated this proportion to be somewhere around 0.20.

(a) Use the given preliminary estimate to determine the sample size required to estimate the proportion of adult Americans who would like an Internet connection in their car to within 0.02 with 95% confidence. (Enter your answer as a whole number.)

(b) The formula for determining sample size given in this section corresponds to a confidence level of 95%. How would you modify this formula if a 99% confidence level was desired?

n = p(1 − p)2.58B2

n = p(1 − p)2.05B2

  

n = p(1 − p)2.33B2

n = p(1 − p)1.96B2

n = p(1 − p)1.645B2

(c) Use the given preliminary estimate to determine the sample size required to estimate the proportion of adult Americans who would like an Internet connection in their car to within 0.02 with 99% confidence. (Enter your answer as a whole number.)

Answer 1

Population proportion ( P )= 0.20

a)

Margin of error (B) = 0.02

confidence level ( C )= 95%

formula for sample size is

Where Zc is the Z critical value for c= 95%

Zc = 1.96

n = 1536.64

n = 1537

Sample size required = 1537

b)

for c= 99% we just want to change the critical value in the formula

z critical value for 99% is = 2.58

hence, formula after modification is

n = p(1 − p)2.58B2

c)

Margin of error (B) = 0.02

confidence level ( C )= 99%

formula for sample size is

Where Zc is the Z critical value for c= 99%

Zc = 2.58

n = 2662.56

n = 2663

Sample size required = 2663