Answered

Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is . The US EIA updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is 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 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 _____.

Sagot :

yoodyannapolis

Answer:

The answer is "23, 62, and 139"

Step-by-step explanation:

In point a:

[tex]\to \sigma = \$0.24\\\\ \to E = \$0.10\\\\ 95\% \text{confidence level of the z}: \\\\\to \alpha = 1 - 95\% = 1 - 0.95 = 0.05\\\\\to \frac{\alpha}{2} = \frac{0.05}{2} = 0.025\\\\\to Z_{\frac{\alpha}{2}} = Z_{0.025} = 1.96\\\\[/tex]

 Calculating the sample size:

[tex]\to n = (\frac{(Z_{\frac{\alpha}{2}} \times \sigma)}{E})^2[/tex]

      [tex]= (\frac{(1.96 \times 0.24 )}{0.10})^2\\\\= 22.13 \approx 23[/tex]

In point b:

[tex]\to \sigma = \$0.24\\\\\to E = \$0.06\\\\\to Z_{\frac{\alpha}{2}} = Z_{0.025} = 1.96\\\\\to n = (\frac{(Z_{\frac{\alpha}{2}} \times \sigma )}{E})^2\\\\[/tex]

      [tex]= (\frac{(1.96 \times 0.24 )}{0.06})^2\\\\= 61.47 \approx 62[/tex]

In point c:

[tex]\to \sigma = \$0.24\\\\\to E =\$0.04\\\\\to Z_{\frac{\alpha}{2}} = Z_{0.025} = 1.96\\\\\to n = (\frac{(Z_{\frac{\alpha}{2}} \times \sigma )}{E})^2\\\\[/tex]

      [tex]= (\frac{(1.96\times 0.24 )}{0.04})^2 \\\\=138.30 \approx 139[/tex]    

We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.