Some Results from a survey administered to a nationally representative sample are reported here in terms of differences by gender. Which of these differences, if, are significant? Write a sentence or two of interaction for each test. a. Proportion favoring the legalization of marijuana: Males Females P s 1 = 0.37 P s 2 = 0.31 N 1 = 202 N 2 = 246 b. Proportion strongly agreeing that “kids are life’s greatest joy”: Males Females P s 1 = 0.47 P s 2 = 0.58 N 1 = 251 N 2 = 351 c. Proportion voting for president Obama in 2012: Males Females P s 1 = 0.45 P s 2 = 0.53 N 1 = 399 N 2 = 509 d. Average hours spent with e-mail each week: Males Females X ¯ 1 = 4.18 X ¯ 2 = 3.38 s 1 = 7.21 s 2 = 5.92 N 1 = 431 N 2 = 535 e. Average rate of church attendance (number of times per year): Males Females X ¯ 1 = 3.19 X ¯ 2 = 3.99 s 1 = 2.60 s 2 = 2.72 N 1 = 641 N 2 = 808 f. Number of children: Males Females X ¯ 1 = 1.49 X ¯ 2 = 1.93 s 1 = 1.50 s 2 = 1.50 N 1 = 635 N 2 = 803

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 8, Problem 8.15P
Textbook Problem
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Some Results from a survey administered to a nationally representative sample are reported here in terms of differences by gender. Which of these differences, if, are significant? Write a sentence or two of interaction for each test.a. Proportion favoring the legalization of marijuana: Males Females P s 1 = 0.37 P s 2 = 0.31 N 1 = 202 N 2 = 246 b. Proportion strongly agreeing that “kids are life’s greatest joy”: Males Females P s 1 = 0.47 P s 2 = 0.58 N 1 = 251 N 2 = 351 c. Proportion voting for president Obama in 2012: Males Females P s 1 = 0.45 P s 2 = 0.53 N 1 = 399 N 2 = 509 d. Average hours spent with e-mail each week: Males Females X ¯ 1 = 4.18 X ¯ 2 = 3.38 s 1 = 7.21 s 2 = 5.92 N 1 = 431 N 2 = 535 e. Average rate of church attendance (number of times per year): Males Females X ¯ 1 = 3.19 X ¯ 2 = 3.99 s 1 = 2.60 s 2 = 2.72 N 1 = 641 N 2 = 808 f. Number of children: Males Females X ¯ 1 = 1.49 X ¯ 2 = 1.93 s 1 = 1.50 s 2 = 1.50 N 1 = 635 N 2 = 803

Expert Solution
To determine

(a)

To find:

The significant difference between two sample proportions.

Explanation of Solution

Given:

The sample statistics is given in the table below,

 Sample 1(Males) Sample 2(Females) Ps1=0.37 Ps2=0.31 N1=202 N2=246

Approach:

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:

The formula to calculate the sampling distribution of the differences in sample proportions of large samples is given by,

Z(obtained)=(Ps1Ps2)(Pu1Pu2)σpp

Where, Ps1 and Ps2 is the proportion of first and second sample respectively,

Pu1 and Pu2 is the proportion of first and second population respectively,

σpp is the standard deviation and the formula to calculate σpp is given by,

σpp=Pu(1Pu)N1+N2N1N2

Where, N1 and N2 is the number of first and second population respectively.

And Ps1 is the population proportion and the formula to Ps1 is given by,

Pu=N1Ps1+N2Ps2N1+N2

Calculation:

As the significant difference in the sample proportions is to be determined, a two tailed test is applied.

Follow the steps for two-sample testing as,

Step 1. Making assumptions and meeting test requirements.

Model:

Independent random samples.

Level of measurement is nominal.

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 samples of the population. Thus, the null and the alternative hypotheses are,

H0:Pu1=Pu2

H1:Pu1Pu2

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

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

Thus, the sampling distribution is Z distribution.

The level of significance is,

α=0.05

Area of critical region is,

Z(critical)=±1.96

Step 4. Computing test statistics.

The population standard deviations are unknown.

The formula to calculate Pu is given by,

Pu=N1Ps1+N2Ps2N1+N2

Substitute 0.37 for Ps1, 0.31 for Ps2, 202 for N1, and 246 for N2 in the above mentioned formula,

Pu=202×0

Expert Solution
To determine

(b)

To find:

The significant difference between two sample proportions.

Expert Solution
To determine

(c)

To find:

The significant difference between two sample proportions.

Expert Solution
To determine

(d)

To find:

The significant difference in the sample statistics of the two samples.

Expert Solution
To determine

(e)

To find:

The significant difference in the sample statistics of the two samples.

Expert Solution
To determine

(f)

To find:

The significant difference in the sample statistics of the two samples.

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