Question

"Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste 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 7 hours with a sample standard deviation of 2.2 hours."

a. Define the random variables X and X- in words.
b. Which distribution should you use for this problem? Explain your choice.
c. Construct a 95% confidence interval for the population mean time wasted.
d. Explain in a complete sentence what the confidence interval means.

Answer 1

See Explanation Below

Explanation:

Given

n = sample size = 81

u = mean wait time = 7 hours

σ = standard deviation = 2.2 hours

a

X is wait time per individual

X- is the mean of the sample means of size 81

b. Normal distribution

It's a distribution that occurs naturally in many situations; and it fits many natural phenomena. an example is given in the question above.

c.

x-bar = 7

To calculate the Margin of Error (ME)

For confidence Interval of 95%, the margin of error M.E = 1.96σ/√n

Where n = 81

M.E = 1.96 * 2.2 /√81

M.E = 0.48

So, the confidence Interval is given as follows

95% CI: 7-0.48 < u < 7+0.48

95% CI: 6.52 < u < 7.48

d. We are 95% confident that the population mean waiting time is

between 6.52 and 7.48 hours