Question

High-power experimental engines are being developed by the Stevens Motor Company for use in its new sports coupe. The engineers have calculated the maximum horsepower for the engine to be 600HP. Nine engines are randomly selected for horsepower testing. The sample has an average maximum HP of 610 with a standard deviation of 50HP. Assume the population is normally distributed. Step 2 of 2 : Use the confidence interval approach to determine whether the data suggest that the average maximum HP for the experimental engine is significantly different from the maximum horsepower calculated by the engineers.

Answer 1

df = n - 1 = 9 - 1 = 8

t critical value at 0.05 level with 8 df = 2.306

95% confidence interval for is

- t * s / sqrt(n) < < + t * s / sqrt(n)

610 - 2.306 * 50 / sqrt(9) < < 610 + 2.306 * 50 / sqrt(9)

571.57 < < 648.43

95% CI is ( 571.57 , 648.43 )

since claimed mean 600 is contained in confidence interval, we do not have sufficient evidence to reject H0.

We conclude at 0.05 level that we fail to support the claim.