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 eight hours with a sample standard deviation of four hours.

A)

I. x¯ = __________ s x

II. sx= __________

III. n = __________

IV. n – 1 = __________

B) Define the random variables X and X¯ in words.

C) Which distribution should you use for this problem? Explain your choice.

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.

Answer 1

A)

Sample mean , $\bar{x}= 8$
Sample standard deviation,   
Sample size, n = 81   
Degrees of freedom , n - 1 = 81 -1 = 80

S 4

B)
x is the time an individual waited.

$\bar{x}$  is the mean waiting time .

C)

In this context we will use t-distribution since population standard deviation is not known.

D)

i) We need to construct the 95% confidence interval for the population mean μ.

The critical value for α=0.05 and df = 80  is t_c =1.99. The corresponding confidence interval is computed as shown below:

S (X - te X +tc X - CI n 4 81.99 V81 4 8-1.99 V81 (7.116, 8.884)

ii)

16 12 A 8 -4 20

iii) The error bound is also known as the margin of error which is the value added and subtract from the mean in the interval which is 0.884 in this context.

iv) A confidence interval gives an estimated range of values which is likely to include an unknown population parameter.

A 95% confidence interval is a range of values that you can be 95% certain that it contains the true mean of the population.