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 660HP. Twenty five engines are randomly selected for horsepower testing. The sample has an average maximum HP of 670 with a standard deviation of 60HP. 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.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 670

sample standard deviation = s = 60

sample size = n = 25

Degrees of freedom = df = n - 1 = 25-1 =24

_{= 0.05 = /2 =0.05/2 =0.025}

t _/2,df = t_{0.025,24 =2.06}

Margin of error = E = t_/2,df * (s /n)

=2.06 * (60 / 25)

Margin of error = E = 24.77

The _{= 0.05} confidence interval estimate of the population mean is,

- E < < + E

670 - 24.77 < < 670 + 24.77

645.23 < < 694.77

(645.23,694.77)