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 710HP. Twenty five engines are randomly selected for horsepower testing. The sample has an average maximum HP of 740 with a standard deviation of 45HP. Assume the population is normally distributed. Step 1 of 2: Calculate a confidence interval for the average maximum HP for the experimental engine. Use a significance level of α=0.05. Round your answers to two decimal places.

Step 2 of 2:

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 710HP. Twenty five engines are randomly selected for horsepower testing. The sample has an average maximum HP of 740 with a standard deviation of 45HP. Assume the population is normally distributed.

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

Solution Step-1: n=25, X= 740 HP, s = 45 HP, x=0.05 The 95% confidence interval for u is given by u It J! at <= 0.05, tn=15ą - t24; d.o = 2.0639 245 0.025 Lower limit =ř - t. trija sa = 740 - 2.0639 x 45 5 = 740 - 2.0639x9 - 740-18.5751 Lower Limit = 721.4249 Upper Limit = X+ t + tnaliza i da 5x45 = 740 + 2.0639 x 45 S - 740 + 18.5751 Upper Limit = 758.5751 : 95% confidence interval for the average maximum Hp for the experimental engine l is (721.4249,758.5751) If Rounded to 2 decimal places, the interval és G721.42,758.58). Given that u = 710 Hpias calculated by engineers. But we can clearly see that 710 < 721.42 (low ey limit of confidence interval. So it is significantly different from the average maximum Hp for the experimental engine. Step-2: