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a. S W Statewide, social workers average 10.2 years of experience. In a random sample, 203 social workers in greater metropolitan Shinbone average only 8.7 years, with a standard deviation of 0.52. Are social workers in Shinbone significantly less experienced? ( NOTE: The wording of the research hypothesis may justify a one-tailed test of significance. For a one -tailed test, what form would the research hypothesis take, and where would the critical region begin? ) b. The same sample of social workers reports an average annual salary of $ 25 , 782 , with a standard deviation of $ 622 . Is this figure significantly higher than the statewide average of $ 24 , 509 ? ( NOTE: The wording of the research hypothesis suggests a one-tailed test. What form would the research hypothesis take, and where would the critical region begin? )

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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 7.3P
Textbook Problem
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a. S W Statewide, social workers average 10.2 years of experience. In a random sample, 203 social workers in greater metropolitan Shinbone average only 8.7 years, with a standard deviation of 0.52. Are social workers in Shinbone significantly less experienced? (NOTE: The wording of the research hypothesis may justify a one-tailed test of significance. For a one -tailed test, what form would the research hypothesis take, and where would the critical region begin?)

b. The same sample of social workers reports an average annual salary of $ 25 , 782 , with a standard deviation of $ 622 . Is this figure significantly higher than the statewide average of $ 24 , 509 ? (NOTE: The wording of the research hypothesis suggests a one-tailed test. What form would the research hypothesis take, and where would the critical region begin?)

Expert Solution
To determine

a)

To find:

The significant difference between the given statements.

Explanation of Solution

Given:

The given information is,

Statewide, social workers average 10.2 years of experience. In a random sample, 203 social workers in greater metropolitan Shinbone average only 8.7 years, with a standard deviation of 0.52.

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¯μσ/N

Where, X¯ is the sample mean,

μ is the population,

σ is the population standard deviation and

N is the sample size.

Calculation:

From the given information, the sample size is 203, sample mean is 8.7 years, population mean is 10.2 years and the population standard deviation is 0.52 years.

Follow the steps for one-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 the average experiences of social workers at Shinbone is equal to the average experience of social workers statewide and the alternative hypothesis is that the average experiences of social workers at Shinbone is less than the average experience of social workers statewide.

Thus, the null and the alternative hypotheses are,

H0:μ=10.2

H1:μ<10.2

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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