Question

# A car company says that the mean gas mileage for its luxury sedan is at least...

A car company says that the mean gas mileage for its luxury sedan is at least 21 miles per gallon​ (mpg). You believe the claim is incorrect and find that a random sample of 7 cars has a mean gas mileage of 19 mpg and a standard deviation of 3 mpg. At alpha equals 0.025​, test the​ company's claim. Assume the population is normally distributed. Which sampling distribution should be used and why? State the appropriate hypothesis to test. What is the standardized test statistic? What is the critical value? What is the outcome and conclusion?

since population standard deviation is unknown and sample size is less than 30,

we assume that population is normally distributed and use student t distribution,

hypothesis test being used is 1 sample t test for mean.

from above test statistic t =-1.764

critical value =-2.447

 since test statistic does not falls in rejection region we fail to reject null hypothesis we do not have have sufficient evidence to conclude that mean gas mileage for its luxury sedan is less than 21 mpg