Question

The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is $3.95. The US EIA updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is $.24 for the price of a gallon of regular gasoline and recommend the appropriate sample size for the US EIA to use if they wish to report each of the following margins of error at 95% confidence. Round up to the next whole number.

a. The desired margin of error is $.10. The appropriate sample size is ____.

b. The desired margin of error is $.06. The appropriate sample size is ____.

c. The desired margin of error is $.04. The appropriate sample size is _____.

Answer 1

Answer:  a. 23   b. 62      c. 139

Step-by-step explanation:

Formula for sample size :-

$n=(\dfrac{z_{\alpha/2}\cdot \sigma}{E})^2$

Given : $\sigma=0.24$

Critical value of 95% confidence : $z_{\alpha/2}=1.96$

a. For E = 0.10

Now, the required sample size will be :-

$n=(\dfrac{1.96\cdot 0.24}{0.10})^2\\\\=22.127616\approx23$

Hence, The appropriate sample size is = 23.

b. For E = 0.06

Now, the required sample size will be :-

$n=(\dfrac{1.96\cdot 0.24}{0.06})^2\\\\=61.4656\approx62$

Hence, The appropriate sample size is = 62.

b. For E = 0.04

Now, the required sample size will be :-

$n=(\dfrac{1.96\cdot 0.24}{0.04})^2\\\\=61.4656\approx62$

Hence, The appropriate sample size is = 139.