The Laughing StockUnitof the New York Comedy Department (NYCD) is considering the purchase of new belly-laugh meters. On average, the laugh-o-meterpresently used by the department can detect a guffaw at a distance listed below. In order to demonstrate the new meters, the manufacturer has allowed the NYCD to use the detectors for a short period of time. A random sample shows the distance at which the new meters can detect a bad joke in feet (mean) with a sample standard deviation. Is the sample meter better or worse than the original meter?

Current laugh-o-meter detection range in feet (population average): 75

New meterdetection range in feet (mean from sample): 100

Standard deviation from sample: 72

Sample size (n): 36

a) State the null and alternative hypothesis.

b) Should the department purchase the new laugh-o-meters?

(You need to calculate a 95% confidence interval, or a t score, but also use your gut to check the answer. Remember the rule that less than 2 standard errors from the mean, the result is not unusual.) Show your work.