Question

A manufacturer of small engines concerned with the issue of noise pollution developed a new engine that would, it was hoped, be quieter than the standard model. 41 of the new models were tested for noise level and with 65 of the standard models. The results are given below with noise measured in decibels.

Sample	Sample Size	Sample Mean	Sample Standard Deviation
Standard Model	65	84	11.6
New model	41	72	9.2

a. Find a 95% confidence interval for the difference in mean decibel levels μ_se -  μ_ne .

b. Do the population means appear to be different at 5% level of significance?

Answer 1

a.

Even though population standard deviations are not known, sample size from both the populations is greater than 30 hence we use z test for finding confidence interval.

b.

Hypothesis:

Since 95% confidence interval does not contain value zero, hence we reject null hypothesis at 5% level of significance. And conclude that there is significant difference between in mean decibel levels.