The Chrysler Corporation is pushing its new Dodge Ram pickup

The Chrysler Corporation is pushing its new Dodge Ram pickup trucks heavily through advertising. One of the critisisms of previous models of the Ram pickup was that they are noisy while driving at highway speeds. Dan Richter is a marketing manager at Chrysler and wants to claim that this year\'s model is quieter than the previous model. He is adamant that research supports that claim before he will go forward with the claim. Chrysler had measured the sound level of last year\'s model and the average sound level was 54 decibels at 55 miles per hour with a standard deviation of 5.8 decibels. The standard deviation is thought to be consistent for the entire population of Ram trucks. A sample of 36 new models yielded an average sound level of 52 decibels at 60 miles per hour.

Conduct an Hypothesis Test that would provide evidence for Chrysler to support the statement that the new model is quieter than last year\'s model.

Identify the Null and Alternate Hypotheses

Use a confidence level of 95%

Solution

Let mu be the population mean

The test hypothesis:

Ho: mu=54 (i.e. null hypothesis)

Ha: mu<54 (i.e. alternative hypothesis)

The test statistic is

Z=(xbar-mu)/(s/vn)

=(52-54)/(5.8/sqrt(36))

=-2.07

It is a left-tailed test.

Given a=0.05, the critical value is Z(0.05) = -1.645 (from standard normal table)

Since Z=-2.07 is less than -1.645, we reject the null hypothesis.

So we can conclude that the new model is quieter than last year\'s model.