Question 939765: A car manufacturer plans on using their current minivan engine in a new line of Sport Utility Vehicles they are developing. The mean fuel consumption rate is dependent on, amongst other things, the vehicle mass, rolling resistance, wind resistance, and driver agressiveness. In an effort to determine the mean highway fuel consumption rate for this vehicle, an engineer sends 25 of the vehicles out on separate highway test routes. The sample mean fuel consumption
rate is determined to be 7.8 ℓ/100 km with a standard deviation of 0.9ℓ/100 km.
(a) Find a 95% confidence interval for the mean highway feul consumption rate for the vehicle.
(b) Suppose that the engineer wants to be 95% confident that the estimated mean highway fuel consumption rate is within 0.1 ℓ/100 km of the true mean highway consumption rate.How many vehicles should be sent out?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! an engineer sends 25 of the vehicles out on separate highway test routes. The sample mean fuel consumption
rate is determined to be 7.8 ℓ/100 km with a standard deviation of 0.9ℓ/100 km.
(a) Find a 95% confidence interval for the mean highway feul consumption rate for the vehicle.
sample mean = x-bar = 7.8
ME = z*s/sqrt(n) = 1.96*0.9/sqrt(25) = 0.353
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95% CI: 7.8-0.353 < u < 7.8+0.353
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(b) Suppose that the engineer wants to be 95% confident that the estimated mean highway fuel consumption rate is within 0.1 ℓ/100 km of the true mean highway consumption rate.How many vehicles should be sent out?
Since ME = z*s/sqrt(n),
n = [z*s/E]^2 = [1.96*0.9/0.1]^2 = 312 when rounded up
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Cheers,
Stan H.
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