Question

The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is $2.94. The US EIA updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is $0.20 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 your answers up to the nearest whole number.) (a) The desired margin of error is $0.10. 16 Changed: Your submitted answer was incorrect. Your current answer has not been submitted. (b) The desired margin of error is $0.06. 43 Correct: Your answer is correct. (c) The desired margin of error is $0.04.

Answer 1

The answer is "16, 43, and 96".

Explanation:

Given:

`\sigma = 0.20\\\\c = 95\% = 0.95\\\\\therefore \alpha = 1- c = 1- 0.95 = 0.05\\\\\therefore (\alpha)/(2) = 0.025\\\\`

Using Z table:

`\therefore Z_{(\alpha)/(2)} = 1.96\\\\`

For point a:

`E = 0.10\\\\n=(\frac{Z_{(\alpha)/(2) * \sigma}}{E})^2`

`= (((1.96* 0.20))/(0.10))^2\\\\= 15.3664 \approx 16`

so, The Sample size (n) = 16

For point b:

`E = 0.06\\\\n=(\frac{Z_{(\alpha)/(2) * \sigma}}{E})^2`

`= (((1.96* 0.20))/(0.06))^2\\\\= 42.6844444444\approx 43`

For point c:

`E = 0.04\\\\n=(\frac{Z_{(\alpha)/(2) * \sigma}}{E})^2`

`= (((1.96* 0.20))/(0.04))^2\\\\= 96.04\approx 96`