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StatisticsEssentials Of Statisticsa. 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? )BuyFind*arrow_forward*

4th Edition

HEALEY + 1 other

Publisher: Cengage Learning,

ISBN: 9781305093836

Chapter 7, Problem 7.3P

Textbook Problem

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**a.**
*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
*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.

**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,

Where,

*N* is the sample size.

**Calculation:**

From the given information, the sample size is 203, sample mean is

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,

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

And area of critical region is

Expert Solution

To determine

b)

**To find:**

The significant difference between the given statements.

Essentials Of Statistics

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