The mean stopping distance for a Jeep Wrangler is 65 feet wh

The mean stopping distance for a Jeep Wrangler is 65 feet (when the car is travelling 45 miles per hour.) The engineering department at Chrysler has designed a new brake system that is thought to be more effective. The new system is installed on 64 cars, and the tests lead to the sample mean of 63.5 feet. Assuming that the population standard deviation is 5 feet, can we conclude at a 1% significance level that the new break system reduces the mean stopping distance? Using the critical value approach, the null hypothesis is rejected if the value of the test statistic

Solution

The null hypothesis would be to check if the braking distance is actually reduced or not.

So,

Ho : BD >= 65

Ha : BD < 65

This, would be a one tailed test.

z-stat = 63.5 - 65 / (5 / sqrt(64))

= -2.400

Since the Z-score is indeed below cutoff point.

Hope this helps.