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Students t test for hypothesis testing

A consumer electronics firm has developed a new type of remote control button that is designed to operate before becoming intermittent. A random sample of 25 of new buttons resulted in a mean of 1,241.2 hours of continuous service with a standard deviation of 110.8 hours. The current best remote control button in the market has a mean life of 1200 hours.

Can we conclude that the new remote control button is superior to the current best product in the market at a 95% confidence level?

Each patient of Aloha Memorial Hospital is asked to evaluate the service at the time of release. Recently there have been complaints that resident physicians and nurses on the surgical wing respond too slowly to calls of senior citizens. In fact, it is claimed that the other patients receive faster service. Mr. Armstrong, president of the hospital, asked the quality assurance department to investigate. After studying the situation, the quality assurance department collected the following data.
Patient Type Sample mean Sample Standard Deviation Sample Size
Senior citizen 5.50 minutes 0.40 minutes 50
Other 5.30 minutes 0.30 minutes 100

Is it reasonable to conclude the mean response time is longer for the senior citizen cases at a 99% confidence level?

Solution Summary

The solution gives complete details of students t test for comparing the the mean life of remote control button with a standard value. Null hypothesis, alternative hypothesis, critical value, test statistic and P value are given.