# 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?

### Essentials Of Statistics

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

### Essentials Of Statistics

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

#### Solutions

Chapter
Section
Chapter 7, Problem 7.7P
Textbook Problem
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## 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.

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