Question

The U.S. Energy Information Administration (US LIA) reported that the average price for a gallon of regular gasoline is $3.98. The US EI updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is 8.24 for the price of a gallon of regular gasoline and recommend the appropriate sample sire 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 8.05. The appropriate sample size is

Answer 1

friven data: let us Assume standard deviation S = 244 S= 24. 0.24 100 where, The Required Sample Size is given by : 2 Zz 2 2 E a) The desired margin of Error is $ 10%. 10 100 0.10 Here, following margin of frrors at (asºl. Confidence So, confidence interval 9547 level of Significance (x) - 1- C.I |- 9541 95 100 I-0.95 0.05 0.05 xa 0.025 2 2 11 at E=0.10 2 2 2 Z (0-24) (0-10) n= Z 20.05 2 E 2 0.0576 (1.968 na 0.01 z [from: 7- Critical value calculator ] (1.96) X 5.76 22.128 - 23 n

614 Coco 0.06 100 b) the desired Margin of Error is at Confidence interval 45*l. level of Signifarice & 0.05 0.05 2 0.025 2 at t = 0.06 2 21 0.05 2 (0:24) (0.06) 2 2 f? (1.96) * 0.0546 E 0.0036 [from: 2 Critical value Calculator +(1.96)2 x 16 3.8416 X 16 5 100 0.05 0.05 -0.025 0.05 2 61. 465 162 c) The desired Margin of frror is $5*. at confidence interval 45'l. level of significance & "at t = 0.05 20.005 (0.24² (0.05) 6.96² 0.0576 [ from 7: Critical value Calculator] 3.8416 X 23:04 n=24 2 € 0.0025 => 88.51 ng 189
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