Question

A car manufacturer claims that the bumper on its cars is constructed in such a way that if the car is driven into a wall at a speed of 15 miles per hour the damage to the car would cost about $200 to fix, on average.  A consumer testing agency wants to check the manufacturer's claim that average (or mean) expenditure for bumper repair is equal to $200 against the alternative hypothesis that mean expenditure is not equal to $200 at a significance level of 0.01.  The agency test crashes 9 cars.  The resulting damages are:

                        245                  305                  175                  250                  280

                        160                  250                  195                  210

            Test the hypothesis and interpret the result.         

The class is market research

Answer 1

Solution: The null and alternative hypotheses are:

Under the null hypothesis, the test statistic is:

Where:

The p-value is:

The p-value is found using the excel file:

Where:

1.862 is the test statistic

8 is the degrees of freedom

2 stands for the two-tailed test.

Conclusion: Since the p-value is greater than the significance level 0.01, we, therefore, fail to reject the null hypothesis and conclude that the mean expenditure is $200