Suppose that a committee is studying whether or not there is excessive time waste in our judicial system. It is interested in the mean amount of time individuals spend at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was 4 hours with a sample standard deviation of 1.2 hours. (a) i. x¯= 8
ii. sx = 4
iii. n = 81
iv. n – 1 = 80
(b) Define the random variables X and X in words.
a. X is the number of individuals at the courthouse to be called for service.
b. X is the average number of individuals at the courthouse.
c. X is the amount of time an individual waits at the courthouse to be called for service.
d. X is the mean wait time for a sample of individuals.
(c) Which distribution should you use for this problem? Explain your choice.
a. The standard normal distribution should be used because the sample standard deviation is known.
b. The standard normal distribution should be used because the population standard deviation is known.
c. The Student's t-distribution for 81 degrees of freedom should be used because the sample standard deviation is known.
d. The Student's t-distribution for 80 degrees of freedom should be used because we do not know the population standard deviation.
(d) Construct a 95% confidence interval for the population mean time wasted.
i. State the confidence interval.
ii. Sketch the graph.
iii. Calculate the error bound.
(e) Explain in a complete sentence what the confidence interval means.