Question

Sharona is asked to do a poll to estimate the underlying mean number of kilometers people drive in their cars in a week to within 1.5 kilometers at a confidence level of 97%. The standard deviation of the number of miles driven by a driver is 29. Sharona needs to figure out how many drivers she should sample.

A. What is the z value she should use? z =  .
Round your z to 4 decimals and use the rounded answer in computing the required sample size.

B. How many drivers should she survey? .

Be sure to round accordingly.

Answer 1

A. What is the z value she should use?

Solution:

We are given

Confidence level = 97%

So, we have

Critical Z value = 2.1701

(by using z-table/excel)

B. How many drivers should she survey? .

The sample size formula is given as below:

n = (Z*σ/E)^2

We are given

σ = 29

Confidence level = 97%

Critical Z value = 2.1701

(by using z-table/excel)

Margin of error = E = 1.5

The sample size is given as below:

n = (Z*σ/E)^2

n = (2.1701*29/1.5)^2

n = 1760.244

Required sample size = 1761