   Chapter 7, Problem 7.8P

Chapter
Section
Textbook Problem

S O C A school system has assigned several hundred "chronic and severe underachievers” to an alternative educational experience. To assess the program, a random sample of 35 has been selected for comparison with all students in the system.a. In terms of GPA, did the program work? Systemwide GPA Program GPA μ = 2.47 X ¯ = 2.55 s = 0.70 N = 35 b. In terms of absenteeism (number of days missed per year), what can be said about the success of the program? Systemwide Program μ = 6.137 X ¯ = 4.78 s = 1.11 N = 35 c. In terms of standardized test scores in math and reading, was the program successful? Math Test--Systemwide Math Test--Program μ = 103 X ¯ = 106 s = 2.0 N = 35 Reading Test--Systemwide Reading Test--Program μ = 110 X ¯ = 113 s = 2.0 N = 35 (HINT. Note the wording of the research questions. Is a one-tailed test justified? Is the program a success if the students in the program are no different from students systemwide? What if the program students were performing at lower levels? If a one tailed test is used, what form should the research hypothesis take? Where will the critical region begin?)

To determine

a)

To find:

The significant difference between the given statements.

Explanation

Given:

The given information is,

A school system has assigned several hundred "chronic and severe underachievers” to an alternative educational experience. To assess the program, a random sample of 35 has been selected for comparison with all students in the system.

The given table of information is,

 Systemwide GPA Program GPA μ=2.47 X¯=2.55s=0.70N=35

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 small samples with single sample mean and unknown standard deviation, the t value is given by,

t(obtained)=X¯μs/N1

Where, X¯ is the sample mean,

μ is the population mean,

s is the estimate population standard deviation and,

N is the sample size.

Calculation:

From the given information, the sample size is 35, sample mean is 2.55, population mean is 2.47 and the sample standard deviation is 0.70.

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 GPA scores between the students under the new program and the students in the system.

Thus, the null and the alternative hypotheses are,

H0:μ=2.47

H1:μ2.47

Step 3. Selecting the sampling distribution and establishing the critical region.

Since, the sample is small, t distribution can be used.

Thus, the sampling distribution is t distribution.

The level of significance is α=0.05

To determine

b)

To find:

The significant difference between the given statements.

To determine

c)

To find:

The significant difference between the given statements.

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