# 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

### 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 7.15P
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

Expert Solution
To determine

a)

To find:

The significant difference between the given statements.

### Explanation of Solution

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

Expert Solution
To determine

b)

To find:

The significant difference between the given statements.

Expert Solution
To determine

c)

To find:

The significant difference between the given statements.

Expert Solution
To determine

d)

To find:

The significant difference between the given statements.

Expert Solution
To determine

e)

To find:

The significant difference between the given statements.

Expert Solution
To determine

f)

To find:

The significant difference between the given statements.

### Want to see the full answer?

Check out a sample textbook solution.See solution

### Want to see this answer and more?

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

See solution

Find more solutions based on key concepts
Show solutions
Fill in the blanks. 5. a. If P1(x1, y1) and P2(x2, y2) are any two distinct points on a nonvertical line L, the...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Add the following signed number: (+4)+(4)

Elementary Technical Mathematics

Perform the indicated operation for the following. 19.

Contemporary Mathematics for Business & Consumers

In Exercises 1-4, perform the operations if possible. [132123][142]

Finite Mathematics for the Managerial, Life, and Social Sciences

Evaluate the integral. 44. 1+exdx

Single Variable Calculus: Early Transcendentals

The general solution to (for x, y > 0) is: a) y = ln x + C b) c) y = ln(ln x + C) d)

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

6. A county in California had 724 corporate tax returns filed. The mean annual income reported was \$161.220 wit...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Laying Phone Cable City A lies on the north bank of a river that is 1 mile wide. You need to run a phone cable ...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

What are the intervals of definition of the general solutions in Problems 1, 7, 15, and 18? Discuss why the int...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)