Question

Part 1) When 500 Rowen College students were surveyed, 110 said they own their car. Find a point estimate for p, the population proportion of students who own their cars. Round your answer to 3 decimal places.

Part 2) We intend to estimate the average driving time of Rowen College commuters. From a previous study, we believe that the average time is 42 minutes with a standard deviation of 11 minutes. We want our 99% confidence interval to have a margin of error of no more than plus or minus 3 minutes. What is the smallest sample size.

Answer 1

Solution:

1 )Given that,

n = 500

x = 110

=x / n = 110 / 500 =0.220

2 )Given that,

standard deviation = =11

margin of error = E = 3

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

Sample size = n = ((Z/2 * ) / E)2

= ((2.576 * 11) / 3)2

= 89

Sample size = 89