Question

Police recorded the average speed of cars driving on a busy street by a school. For a sample of 36 ​speeds, it was determined that the average amount over the speed limit for the 36 speeds was 12.3 mph with a standard deviation of 9 mph. The 95 ​% confidence interval estimate for this sample is 9.25 mph to 15.35 mph. ​a) What is the margin of error for this​ problem? ​b) What size sample is needed to reduce the margin of error to no more than plus or minus 2 ​? ​a) The margin of error is nothing mph. ​b) The sample size should be at least nothing speeds.

Answer 1

Solution :

Given that

Point estimate = sample mean = = 12.3

sample standard deviation = s = 9

sample size = n = 36

Confidence interval = 9.25, 15.35

a) Margin of error = E = Upper confidence interval -   

Margin of error = E = 15.35 - 12.3

Margin of error = E = 3.05 mph

b) Margin of error = E =

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z_/2 = 1.96

sample size = n = [Z_/2* / E] ²

n = [1.96 * 9 / 2 ]²

n = 77.79

Sample size = n = 78