close solutoin list

a. S O C Statewide, the population as a whole watches 6.2 hours of TV per day. A random sample of 1017 senior citizens in the state reports watching an average of 5.9 hours per day, with a standard deviation of 0.7. Is the difference significant? b. The same sample of senior citizens reports that they belong to an average of 2.1 voluntary organizations and clubs, with a standard deviation of 0.5. Statewide, the average is 1.7. Is the difference significant?

BuyFind

Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
BuyFind

Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

Solutions

Chapter
Section
Chapter 7, Problem 7.7P
Textbook Problem
55 views

a. S O C Statewide, the population as a whole watches 6.2 hours of TV per day. A random sample of 1017 senior citizens in the state reports watching an average of 5.9 hours per day, with a standard deviation of 0.7. Is the difference significant?

b. The same sample of senior citizens reports that they belong to an average of 2.1 voluntary organizations and clubs, with a standard deviation of 0.5. Statewide, the average is 1.7. Is the difference significant?

Expert Solution
To determine

a)

To find:

The significant difference between the given statements.

Explanation of Solution

Given:

The given information is,

Statewide, the population as a whole watches 6.2 hours of TV per day. A random sample of 1017 senior citizens in the state reports watching an average of 5.9 hours per day, with a standard deviation of 0.7.

The five step model for hypothesis testing is:

Step 1. Making assumptions and meeting test requirements.

Step 2. Stating the null hypothesis.

Step 3. Selecting the sampling distribution and establishing the critical region.

Step 4. Computing test statistics.

Step 5. Making a decision and interpreting the results of the test.

Formula used:

For large samples with single mean and given standard deviation, the Z value is given by,

Z(obtained)=X¯μs/N1

Where, X¯ is the sample mean,

μ is the population,

s is the sample standard deviation and

N is the sample size.

Calculation:

From the given information, the sample size is 1017, sample mean is 5.9, population mean is 6.2 and the sample standard deviation is 0.7.

Follow the steps for two-tailed hypothesis testing as,

Step 1. Making assumptions and meeting test requirements.

Model:

Random sampling.

Level of measurement is interval ratio.

Sampling distribution is Normal.

Step 2. Stating the null hypothesis.

The statement of the null hypothesis is that there is no significant difference in the average hours of watching TV per day between senior citizens and state average.

Thus, the null and the alternative hypotheses are,

H0:μ=6.2

H1:μ6.2

Step 3. Selecting the sampling distribution and establishing the critical region.

Since, the sample is large, a normal curve can be used.

Thus, the sampling distribution is Z distribution.

The level of significance is α=0.05.

And area of critical region is Z(critical)=±1

Expert Solution
To determine

b)

To find:

The significant difference between the given statements.

Want to see this answer and more?

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

See solution

Additional Math Textbook Solutions

Find more solutions based on key concepts
Show solutions
Prove that cosine is a continuous function.

Calculus: Early Transcendentals

Use the guidelines of this section to sketch the curve. y=x2x2

Single Variable Calculus: Early Transcendentals, Volume I

In Exercises 6372, evaluate the expression. 72. 2334

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Graph 42i. a. b. c. d.

Trigonometry (MindTap Course List)

Does a square have a an incenter? b a circumcenter?

Elementary Geometry for College Students

The graph at the right has equation:

Study Guide for Stewart's Multivariable Calculus, 8th

True or False: limx6x3+8x29x+75x34x+30=limx6x35x3.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Secant Lines Find the equation of the secant line for the graph of y=x3fromx=1tox=3. See Figure 3.77. FIGURE 3....

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Samples of size 5 provided the following 20 sample means for a production process that is believed to be in con...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

In Problems 3564 solve the given differential equation by undetermined coefficients. 36. 2y7y+5y=29

A First Course in Differential Equations with Modeling Applications (MindTap Course List)