Book edition OER 2018

Author(s) Barbara Illowsky, Susan Dean

Pages 902 pages

ISBN 9781938168208

Answers without the blur.

Just sign up for free and you're in.

Short Answer

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.
$a . i . x ̄ =i i . s x =i i i . n =i v . n - 1 =$
b. Define the random variables $X a n d X ̄$ 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.

(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 $\bar{X}$ .

(d) The result is :

i. CI= $(7.1155, 8.8845)$

ii. the graph is shown

iii. $0.8844$

(e) The $95 %$ confidence that the interval between $7.11 a n d 8.88$ minutes accurately represents the true mean courthouse wait time.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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 $81 i s X$ , and the amount of time the single waste at the courts is called for service duty is $X$ .

Step 3: Explanation (c)

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

$t 81 - 1 = t 80$ .

Step 4: Explanation (d)

i. State the confidence interval.

The output of the confidence interval,

C.I = $(7.1155, 8.8845)$

ii. The graph is as follows:

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

$E B M = t_{n - 1} (\frac{α}{2}) \frac{s}{\sqrt{n}}$

$E B M = t_{81 - 1} (\frac{0.05}{2}) \frac{4}{\sqrt{81}}$

$E B M = 0.8844$ .

Step 5: Explanation (e)

The $95 %$ confidence that the interval between $7.11 a n d 8.88$ minutes accurately represents the true mean courthouse wait time.

Find Study Materials for

Create Study Materials

Select your language

Introductory Statistics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Explanation (a)

Step 2: Explanation (b)

Step 3: Explanation (c)

Step 4: Explanation (d)

Step 5: Explanation (e)

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Introductory Statistics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Explanation (a)

Step 2: Explanation (b)

Step 3: Explanation (c)

Step 4: Explanation (d)

Step 5: Explanation (e)

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths