Solution Found!

Business / Statistics for Business and Economics 12 / Chapter 6 / Problem 27E

Statistics for Business and Economics | 12th Edition | ISBN: 9780321826237 | Authors: James T. McClave, P. George Benson, Terry T Sincich

Change Question

The following random sample was selected from a normal

Chapter 6, Problem 27E

(choose chapter or problem)

Get Unlimited Answers

QUESTION:

Problem 27E

The following random sample was selected from a normal distribution: 4, 6, 3, 5, 9, 3.

a. Construct a 90% confidence interval for the population mean μ.

b. Construct a 95% confidence interval for the population mean μ.

c. Construct a 99% confidence interval for the population mean μ.

d. Assume that the sample mean x and sample standard deviation s remain exactly the same as those you just calculated but are based on a sample of n = 25 observations rather than n = 6 observations. Repeat parts a–c. What is the effect of increasing the sample size on the width of the confidence intervals?

Questions & Answers

QUESTION:

Problem 27E

The following random sample was selected from a normal distribution: 4, 6, 3, 5, 9, 3.

a. Construct a 90% confidence interval for the population mean μ.

b. Construct a 95% confidence interval for the population mean μ.

c. Construct a 99% confidence interval for the population mean μ.

d. Assume that the sample mean x and sample standard deviation s remain exactly the same as those you just calculated but are based on a sample of n = 25 observations rather than n = 6 observations. Repeat parts a–c. What is the effect of increasing the sample size on the width of the confidence intervals?

ANSWER:

Solution:

Step 1 of 5:

We have random samples from the Normal distribution.

x	${x}^{2}$
4	16
6	36
3	9
5	25
9	81
3	9
$\Sigma{}x$ = 30	$\Sigma{}{x}^{2}$ = 176

Mean = $\frac{\Sigma{}{x}_{i}}{n}$

= $\frac{30}{6}$

= 5

Variance = $\frac{\Sigma{}{x}^{2}\ -\ \frac{(\Sigma{}{x)}^{2}}{n}}{n-1}$

= $\frac{176\ -\ \frac{({30)}^{2}}{6}}{6-1}$

= $\frac{176\ -\ 150}{5}$

= 5.2

$\sigma{}$ = $\sqrt{5.2}$

= 2.280

Study Tools You Might Need

Chapter: 3 Problem: 16

College Physics 1
Problem 16CQ During a lecture demonstration, a professor places two coins on the edge of a table. She then flicks one of the coins horizontally off the table, simultaneously nudging the other over the edge. Describe the subsequent motion of the two coins, in particular discussing whether they hit

Chapter: 3 Problem: 61

College Physics 1
Problem 61PE A sandal is dropped from the top of a 15.0-m-high mast on a ship moving at 1.75 m/s due south. Calculate the velocity of the sandal when it hits the deck of the ship: (a) relative to the ship and (b) relative to a stationary observer on shore. (c) Discuss how the answers give a consist

Chapter: Problem: 9

Myers' Psychology for AP 2
Which of the following is a positive correlation? a. As study time decreases, students achieve lower grades. b. As levels of self-esteem decline, levels of depression increase. c. People who exercise regularly are less likely to be obese. d. Gas mileage decreases as vehicle weight increases. e. Repea

Chapter: 4 Problem: 34

Elementary Statistics: A Step by Step Approach 8th ed. 8
Computer Ownership At a local university 54.3% of incoming first-year students have computers. If 3 students are selected at random, find the following probabilities. a. None have computers. 0.0954 b. At least one has a computer. 0.9046 c. All have computers. 0.1601

Chapter: 2 Problem: 2.16

Organic Chemistry 3
Which compound in each pair of isomers is the stronger acid? a. CH3CH2CH2NH2 or (CH3)3N b. CH3CH2OCH3 or CH3CH2CH2OH

Chapter: 17 Problem: 34

Anatomy & Physiology 1
Athletes may take synthetic EPO to boost their ________. a. blood calcium levels b. secretion of growth hormone c. blood oxygen levels d. muscle mass

Chapter: 10 Problem: 6

Urban Economics 8
New Sellwood Bridge? Consider the issue of replacing the Sellwood Bridge in Portland, Oregon. The existing bridge has a free-fl ow capacity of 600 vehicles, and the private trip cost at this traffi c volume is $2. Given the equilibrium volume of 1,000 vehicles per hour, the private trip cost is $3. T

Chapter: 21 Problem: 3

Principles of Economics 9
At two points on an indifference curve, a. the consumer has the same income. b. the consumer has the same marginal rate of substitution. c. the bundles of goods cost the consumer the same amount. d. the bundles of goods yield the consumer the same satisfaction.

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

×

Register

Sign up for access to all content on our site!

Or login if you already have an account