   Chapter 7, Problem 7.15P

Chapter
Section
Textbook Problem

S O C / S W A researcher has compiled a file of information on a random sample of 317 families that have chronic, long-term patterns of child abuse. Reported here are some of the characteristics of the sample, along with values for the city as a whole. For each trait, test the null hypothesis of "no difference” and summarize your Findings. Variable City Sample a. Mother’s educational level (proportion completing high school) P u = 0.65 P s = 0.61 b. Family size (proportion of families with four or more children) P u = 0.21 P s = 0.26 c. Mother’s work status (proportion of mothers with jobs outside the home) P u = 0.51 P s = 0.27 d. Relations with kin (proportion of families that have contact with kin at least once a week) P u = 0.82 P s = 0.43 e. Father’s educational achievement (average years of formal schooling) μ = 12.3 X ¯ = 12.5 s = 1.7 f. Father’s occupational stability (average years in preset job) μ = 5.2 X ¯ = 3.7 s = 0.5

To determine

a)

To find:

The significant difference between the given statements.

Explanation

Given:

The given information is,

A researcher has compiled a file of information on a random sample of 317 families that have chronic, long-term patterns of child abuse. Reported here are some of the characteristics of the sample, along with values for the city as a whole.

The given table of information is,

 Variable City Sample a. Mother’s educational level (proportion completing high school) Pu=0.65 Ps=0.61

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 sample proportions, the Z value is given by,

Z(obtained)=PsPuPu(1Pu)/N

Where, Ps is the sample proportion,

Pu is the population proportion and,

N is the sample size.

Calculation:

From the given information, the sample size is 317, sample proportion is 0.61 and the population proportion is 0.65.

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 the proportion of mother’s from the sample completing high school is not significantly different from the population.

Thus, the null and the alternative hypotheses are,

H0:Pu=0.65

H1:Pu0.65

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

Since, the sample is large, Z distribution can be used.

The information given is in the form of proportions, the test for proportion can be used

To determine

b)

To find:

The significant difference between the given statements.

To determine

c)

To find:

The significant difference between the given statements.

To determine

d)

To find:

The significant difference between the given statements.

To determine

e)

To find:

The significant difference between the given statements.

To determine

f)

To find:

The significant difference between the given statements.

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