a psychology research team was interested to study the reaction time of university students. They took a random sample of 100 students from across the university and administered a series of test to determine the reaction time. The observed mean 27.35 seconds and standard deviation 6.31 seconds.

a. what is the sampling distribution of the sample mean? Justify the answer

b. find a 95% confidence interval for the mean reaction time of all university students

c. give the correct interpretation of the above confidence interval

d. calculate the margin of error for 99% confidence interval for the mean reaction time. What is the width of the 99% confidence interval?

e. if the population standard deviation is 8 seconds, what sample size would be required to produce a 95% confidence interval for the population mean reaction time with a margin of error of 1.50 seconds?