An automotive company would like to install a new breaking system in one of its least popular vehicles. The new breaking system promises to be more effective by stopping sooner. To test this claim, the company gathers a sample of 40 cars with the old breaking system and finds that the mean stopping distance is 66 feet with a standard deviation of 4.5 feet. A different sample of the same car model was tested with the new breaking system. This sample of 50 observations yielded a sample mean of 64 feet with a standard deviation of 5 feet.

a. Set up null and alternative hypotheses.

b. Test at the .05 level. What is your conclusion?

c. Would we change our conclusion if we tested at the 0.01 level? Why or why not?

d. For this situation, identify the Type I and Type II errors and the potential issues associated with making each type of error. From a business perspective, which error is worse? What about from the consumer perspective?