Concept explainers
(a)
To find:
The significant difference between two sample proportions.
Answer to Problem 8.15P
Solution:
There is no significant difference between the sample statistics of two samples proportions and it is concluded that there is no sufficient evidence to conclude that male and females differ in favor of legalization of marijuana.
Explanation of Solution
Given:
The sample statistics is given in the table below,
Sample 1 (Males) |
Sample 2 (Females) |
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,
Where,
Where,
And
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,
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,
Area of critical region is,
Step 4. Computing test statistics.
The population standard deviations are unknown.
The formula to calculate
Substitute 0.37 for
The formula to calculate
From equation
Simplify further,
The sampling distribution of the differences in sample proportion for large samples is given by,
Under null hypothesis,
Substitute 0 for
From equation
Thus, the obtained Z value is
Step 5. Making a decision and interpreting the results of the test.
Compare the test statistic with the critical
Conclusion:
Therefore, there is no significant difference between the sample statistics of two samples proportions and it is concluded that there is no sufficient evidence to conclude that male and females differ in favor of legalization of marijuana.
(b)
To find:
The significant difference between two sample proportions.
Answer to Problem 8.15P
Solution:
There is a significant difference between the sample statistics of two samples proportions and it is concluded that females strongly agree that kids are life’s greatest joy.
Explanation of Solution
Given:
The sample statistics is given in the table below,
Sample 1 (Males) |
Sample 2 (Females) |
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,
Where,
Where,
And
Calculation:
As the significant difference in the sample proportions is to be determined, a one 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,
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,
Area of critical region is,
Step 4. Computing test statistics.
The population standard deviations are unknown.
The formula to calculate
Substitute 0.47 for
The formula to calculate
From equation
Simplify further,
The sampling distribution of the differences in sample proportion for large samples is given by,
Under null hypothesis,
Substitute 0 for
From equation
Thus, the obtained Z value is
Step 5. Making a decision and interpreting the results of the test.
Compare the test statistic with the critical
Conclusion:
Therefore, there is a significant difference between the sample statistics of two samples proportions and it is concluded that females strongly agree that kids are life’s greatest joy.
(c)
To find:
The significant difference between two sample proportions.
Answer to Problem 8.15P
Solution:
There is a significant difference between the sample statistics of two samples proportions and it is concluded that males and females differ in opinion for voting Obama in 2012.
Explanation of Solution
Given:
The sample statistics is given in the table below,
Sample 1 (Males) |
Sample 2 (Females) |
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,
Where,
Where,
And
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,
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,
Area of critical region is,
Step 4. Computing test statistics.
The population standard deviations are unknown.
The formula to calculate
Substitute 0.45 for
The formula to calculate
From equation
Simplify further,
The sampling distribution of the differences in sample proportion for large samples is given by,
Under null hypothesis,
Substitute 0 for
From equation
Thus, the obtained Z value is
Step 5. Making a decision and interpreting the results of the test.
Compare the test statistic with the critical
Conclusion:
Therefore, there is a significant difference between the sample statistics of two samples proportions and it is concluded that males and females differ in opinion for voting Obama in 2012.
(d)
To find:
The significant difference in the sample statistics of the two samples.
Answer to Problem 8.15P
Solution:
There is a significant difference between the sample statistics of two samples and it is concluded that males spent more hours at e-mail each week.
Explanation of Solution
Given:
The sample statistics is given in the table below,
Sample 1 (Males) |
Sample 2 (Females) |
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 means is given by,
Where,
Where,
Calculation:
As the significant difference in the sample statistics is to be determined, a one 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 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 sample s of the population. Thus, the null and the alternative hypotheses are,
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,
Area of critical region is,
Step 4. Computing test statistics.
The population standard deviations are unknown.
The formula to calculate
Substitute 7.21 for
Simplify further,
The sampling distribution of the differences in sample means is given by,
Under the null hypotheses,
Substitute
From equation
Thus, the obtained Z value is
Step 5. Making a decision and interpreting the results of the test.
Compare the test statistic with the critical
Conclusion:
Therefore, there is a significant difference between the sample statistics of two samples and it is concluded that males spent more hours at e-mail each week.
(e)
To find:
The significant difference in the sample statistics of the two samples.
Answer to Problem 8.15P
Solution:
There is a significant difference between the sample statistics of two samples and it is concluded that male has less average rate of church attendance compared to females.
Explanation of Solution
Given:
The sample statistics is given in the table below,
Sample 1 (Males) |
Sample 2 (Females) |
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 means is given by,
Where,
Where,
Calculation:
As the significant difference in the sample statistics is to be determined, a one 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 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 sample s of the population. Thus, the null and the alternative hypotheses are,
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,
Area of critical region is,
Step 4. Computing test statistics.
The population standard deviations are unknown.
The formula to calculate
Substitute 2.60 for
Simplify further,
The sampling distribution of the differences in sample means is given by,
Under the null hypotheses,
Substitute
From equation
Thus, the obtained Z value is
Step 5. Making a decision and interpreting the results of the test.
Compare the test statistic with the critical
Conclusion:
Therefore, there is a significant difference between the sample statistics of two samples and it is concluded that male has less average rate of church attendance compared to females.
(f)
To find:
The significant difference in the sample statistics of the two samples.
Answer to Problem 8.15P
Solution:
There is a significant difference between the sample statistics of two samples and it is concluded that males prefer lesser number of children than females.
Explanation of Solution
Given:
The sample statistics is given in the table below,
Sample 1 (Males) |
Sample 2 (Females) |
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 means is given by,
Where,
Where,
Calculation:
As the significant difference in the sample statistics is to be determined, a one 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 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 sample s of the population. Thus, the null and the alternative hypotheses are,
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,
Area of critical region is,
Step 4. Computing test statistics.
The population standard deviations are unknown.
The formula to calculate
Substitute 1.50 for
Simplify further,
The sampling distribution of the differences in sample means is given by,
Under the null hypotheses,
Substitute
From equation
Thus, the obtained Z value is
Step 5. Making a decision and interpreting the results of the test.
Compare the test statistic with the critical
Conclusion:
Therefore, there is a significant difference between the sample statistics of two samples and it is concluded that males prefer lesser number of children than females.
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Chapter 8 Solutions
Essentials Of Statistics
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt