The following are the miles-per-gallon figures for a sample of cars of the same model tested under identical conditions: 22, 38, 28, 29, 24, 25, 27, 28, 29, 28, 27, 31, 33.
a) The consumers' group that conducted this test is skeptical of the manufacturer's claim that its cars average 28 mpg. The group will only publish a rejection of the manufacturer's claim if it can be 99% sure that it is correct in doing so. Specify the null and alternative hypotheses for this test, determine the critical region, and decide whether to reject the manufacturer's claim.
b) Find the 95% confidence interval for the mean gas mileage for cars of this model.
c) Interpret the confidence interval you found in (b).
d) Can you conclude that 95% of all cars of this model will have mpg values within this interval? Explain.