Knowing That a Particular Laboratory Decision Task Takes the Average

Knowing that a particular laboratory decision task takes the average person 2.5 seconds,an experimenter found that 30 randomly selected 80 year olds had a mean response time of 2.7 seconds with an estimated population standard deviation of 1.4 seconds.Using the .05 significance level,is the mean response time of older people slower than the response time of people in general?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Explain the logic of what you did to a person who is familiar with hypothesis testing with a known population variance and a single sample,but who knows nothing about t tests of any kind (for example,you do not need to describe the steps or logic of hypothesis testing).Be sure you explain how this problem differs from a problem with a known population variance and a single sample.Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and all the figuring you did to determine those characteristics.