An earlier study claimed that U.S. adults spent an average of 114 minutes per day with their family. A recently taken sample of 25 adults from a city showed that they spend an average of 109 minutes per day with their family. The sample standard deviation is 11 minutes. Assume that the times spent by adults with their family have an approximate normal distribution.
a. Using a 1% significance level, test whether the mean time spent currently by all adults with their families in this city is different from 114 minutes a day.
b. Suppose the probability of making a Type I error is zero. Can you make a decision for the test of part a without going through the five steps of hypothesis testing? If yes, what is your decision?
Explain.