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Q.106

Expert-verified
Found in: Page 486

### Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208

# Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested inthe mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomlysurveyed $81$ people who recently served as jurors. The sample mean wait time was eight hours with a sample standarddeviation of four hours.$a.i.x̄=__________\phantom{\rule{0ex}{0ex}}ii.sx=__________\phantom{\rule{0ex}{0ex}}iii.n=__________\phantom{\rule{0ex}{0ex}}iv.n–1=__________$b. Define the random variables $XandX̄$ 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.

(a) The Final Result we get,

i. $8$

ii. $4$

iii.$81$

iv $80$

(b) The average wait time for the sample size of X, and the amount of time the single waste at the courts is called for service duty is $\stackrel{-}{X}$ .

(c) The random distribution with the parameters ${t}_{81-1}={t}_{80}$ is used.

(d) The result is :

i. CI=$\left(7.1155,8.8845\right)$

ii. the graph is shown

iii. $0.8844$

(e) The $95%$ confidence that the interval between $7.11and8.88$ minutes accurately represents the true mean courthouse wait time.

See the step by step solution

## Step 1: Explanation (a)

1. The average waiting time in the sample is 8 hours.

$x=8$ hours overline

ii. Waiting time standard deviation, ${s}_{x}=4$

iii. There are $81$ surveyors who have recently served.

iv. If the total number of people questioned the value is

$n-1=80.$

## Step 2: Explanation (b)

The average wait time for the sample size of $81isX$, and the amount of time the single waste at the courts is called for service duty is $\overline{)X}$.

## Step 3: Explanation (c)

The random distribution with the parameters $ln-1$is used. .

$t81-1=t80$.

## Step 4: Explanation (d)

i. State the confidence interval.

The output of the confidence interval,

C.I = $\left(7.1155,8.8845\right)$

ii. The graph is as follows:

iii. The formula is used to compute the error bound.

$EBM={t}_{n-1}\left(\frac{\alpha }{2}\right)\frac{s}{\sqrt{n}}$

$EBM={t}_{81-1}\left(\frac{0.05}{2}\right)\frac{4}{\sqrt{81}}$

$EBM=0.8844$.

## Step 5: Explanation (e)

The $95%$ confidence that the interval between $7.11and8.88$ minutes accurately represents the true mean courthouse wait time.