# a. The students at Littlewood Regional High School cut an average of 3.3 classes per month. A random sample of 117 seniors averages 3.8 cuts per month, with a standard deviation of 0.53. Are seniors significantly different from the student body as a whole? ( HINT: The wording of the research question suggests a two-tailed test. This means that the alternative, or research, hypothesis in step 2 will be stated as H 1 : μ ≠ 3.3 and that the critical region will be split between the upper and lower tails of the sampling distribution. See Table 7.3 for values of Z(critical) for various alpha levels .) b. What if the research question were changed to "Do seniors cut a significantly greater number of classes"? How would the test conducted in problem 7.2a change? ( HINT: This wording implies a one-tailed test of significance. How would the research hypothesis change? For the alpha you used in problem 7.2a, what would the value of Z(critical) be? )

### 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 7.2P
Textbook Problem
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## a. The students at Littlewood Regional High School cut an average of 3.3 classes per month. A random sample of 117 seniors averages 3.8 cuts per month, with a standard deviation of 0.53. Are seniors significantly different from the student body as a whole? (HINT: The wording of the research question suggests a two-tailed test. This means that the alternative, or research, hypothesis in step 2 will be stated as H 1 : μ ≠ 3.3 and that the critical region will be split between the upper and lower tails of the sampling distribution. See Table 7.3 for values of Z(critical) for various alpha levels.)b. What if the research question were changed to "Do seniors cut a significantly greater number of classes"? How would the test conducted in problem 7.2a change? (HINT: This wording implies a one-tailed test of significance. How would the research hypothesis change? For the alpha you used in problem 7.2a, what would the value of Z(critical) be?)

Expert Solution
To determine

a)

To find:

The significant difference between the given statements.

### Explanation of Solution

Given:

The given information is,

The students at Littlewood Regional High School cut an average of 3.3 classes per month. A random sample of 117 seniors averages 3.8 cuts per month, with a standard deviation of 0.53.

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 117, sample mean is 3.8, population mean is 3.3 and the population standard deviation is 0.53.

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 number of cuts of classes between students and seniors.

Thus, the null and the alternative hypotheses are,

H0:μ=3.3

H1:μ3.3

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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