Dylan Jones kept careful records of the fuel efficiency of his new car. After th

Question

Dylan Jones kept careful records of the fuel efficiency of his new car. After the frst seven times he filled up the tank, he found the mean was 24.1 mlles per gallon (mpg) with a sample standard deviation of 0.6 mpg a. Compute the 95% confidence interval for his mpg (Use tDistribution Table) (Round your answers to 3 decimal places) b. How many times should he fill his gas tank to obtain a margin of error below o.05 mpg? (Use z Distribution Table) (Round your answer to the next whole number.) Sample size

Explanation / Answer

ANSWER:

1) Confidence interval = x bar +- z * ( std / (n) ^ 1/2 )

x bar = 24.1

z = 1.96 ( from table)

std = 0.6 mpg

n = 7

confidence interval = 24.1 + - 1.96 * ( 0.6 / (7) ^ 1/2)

ci = 24.1 +- 1.96 * ( 0.6 / 2.6457)

ci = 24.1 + - 1.96 * 0.2267

ci = 24.1 + - 0.4444

ci = (24.54 , 23.655)

2) moe = z score * (std / (n) ^ 1/2)

0.05 = 1.96 * (0.6 / (n) ^ 1/2)

(n) ^ 1/2 = (1.96 * 0.6) / 0.05

(n) ^ 1/2 = 1.176 / 0.05

(n) ^ 1/2 = 23.52

squaring both sides we get

n = 553.19

so the sample size should be more then that 553.19 that is 554.

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