Question

The chief Financial Officer (CFO) for a company with a large fleet of cars regularly used for company business is concerned about gas consumption during the many trips for which these company cars are used. In an effort to investigate the fuel efficiency of the company fleet cars, the CFO randomly selects the fifty trips for which company cars are used and the CFO determines that the gas mileage for thee trips is, on average, 25.02 miles per gallon with a standard deviation of 4.83 miles per gallon. A) The CFO wants to determine the 99% confidence interval for the average gas mileage for the compacts fleet of cars. Should the CFO use the standard normal distribution or the t-distribution. Provide the evidence which supports your response. B) Construct and state the 99% confidence interval for the average gas mileage for the compacts fleet of cars. C) Using one sentence interpret the 99% confidence interval in the context of this scenario.

Answer 1

Here

sample mean

sample standard deviation

and sample size

a) Since population standard deviation is not known, so one should use t distribution.

b) a 99% confidence interval for the average gas mileage for the compacts fleet of cars

Interpretation : Out of 100 samples drawn, mean of these samples will lie between with probability 0.99.