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 810HP. Sixteen engines are randomly selected for horsepower testing. The sample has an average maximum HP of 890 with a standard deviation of 85HP. 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=0.01. Round your answers to two decimal places.

Answer 1

Answer:

The confidence interval for the average maximum HP for the experimental engine is between 639.53HP and 1140.47HP

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 16 - 1 = 15

0.01 significance level.

So a 1 - 0.01 = 0.99 = 99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 15 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.99}{2} = 0.995$. So we have T = 2.9467

The margin of error is:

M = T*s = 2.9467*85 = 250.47

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 890 - 250.47 = 639.53HP

The upper end of the interval is the sample mean added to M. So it is 890 + 250.47 = 1140.47HP

The confidence interval for the average maximum HP for the experimental engine is between 639.53HP and 1140.47HP