# S O C Statewide, the average score on the verbal portion of the college entrance exam is 453, with a standard deviation of 95. A random sample of 137 seniors at Littlewood Regional High School shows a mean score of 502. Is there a significant difference?

### 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 7.4P
Textbook Problem
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## S O C Statewide, the average score on the verbal portion of the college entrance exam is 453, with a standard deviation of 95. A random sample of 137 seniors at Littlewood Regional High School shows a mean score of 502. Is there a significant difference?

Expert Solution
To determine

To find:

The significant difference between the given statements.

### Explanation of Solution

Given:

The given information is,

Statewide, the average score on the verbal portion of the college entrance exam is 453, with a standard deviation of 95. A random sample of 137 seniors at Littlewood Regional High School shows a mean score of 502.

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 137, sample mean is 502, population mean is 453 and the population standard deviation is 95.

Follow the steps for 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 between the verbal portion scores of Littlewood Regional school and state.

Thus, the null and the alternative hypotheses are,

H0:μ=453

H1:μ453

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

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