Question 1

A random sample of 5 scores is collected with a sample mean of 8 and a sample variance of 9. Test the following hypotheses at the .05 level of significance:

$\begin{array}{l}
H_{0}: \sigma^{2}=5 \
H_{1}: \sigma^{2} \neq 5
\end{array}$

Accepted Answer

Degrees of freedom (v) are equal to n -1, thus 5 - 1 = 4. 
The hypothesized populati on variance is provided to us (5). Plugging these values into the formula, we find the test statistic value
 $\chi^{2}=\frac{v s^{2}}{\sigma_{0}^{2}}=\frac{7(9)}{4}=15.75$ 
From Appendix Table 3, and using an alpha level of .05 (i.e., tabled values listed under .975 and .025) and degrees of freedom (v) of 7, we determine the critical values to be.484419 and 11.1433. As the test statistic (15.75)exceeds one of the critical values, our decision is to reject the null hypothesis.

Question 2

A random sample of 9 scores is collected with a sample mean of 62 and a sample variance of 16. Test the following hypotheses at the .05 level of significance:

$\begin{array}{l}
H_{0}: \sigma^{2}=15 \
H_{1}: \sigma^{2} \neq 15
\end{array}$

Accepted Answer

Degrees of freedom (v) are equal to _n_-_{1, thus 9}_{- 1}_{= 8}_{.
The hypothesized populati}_{on variance is provided to us (15}_{). Plugging these values into the formula, we find the test statistic value:} $x^{2}=\frac{v s^{2}}{\sigma_{0}^{2}}=\frac{8(16)}{15}=8.53$ _{From Appendix Table 3, and using an alpha level of .05}_{(i.e., tabled values listed under .975 and .025)}_{and degrees of freedom (}_v_{) of}₈_{, we determine the critical values to be}_2.17973_and_17.5345_{. As t}_{he test}_{statistic (8.53}₎_does_{not exceed}_{one of the critic}_al_values_{, our decision is to}_{fail to}_{reject the null hypothesis.}

Question 3

In what is a researcher interested when conducting a test of inference for independent variances?

Accepted Answer

A)  Whether the population variance for one group is different than the population variance for one or more other independent groups 
B)  Whether the population variance for one group is different than the population variance for one or more other dependent groups 
C)  Whether the population mean difference for one group is different than a hypothesized value 
D)  Whether the sample mean of group 1 differs from the sample mean of group 2 
E)  Whether the population standard deviation is within a ratio of 1:4
F) Whether two groups have the same population mean and variance 
A)  Whether the population variance for one group is different than the population variance for one or more other independent groups 
B)  Whether the population variance for one group is different than the population variance for one or more other dependent groups 
C)  Whether the population mean difference for one group is different than a hypothesized value 
D)  Whether the sample mean of group 1 differs from the sample mean of group 2 
E)  Whether the population standard deviation is within a ratio of 1:4
F) Whether two groups have the same population mean and variance A

Question 4

The following summary statistics are available for two dependent random samples:

s12 = 36, s22 = 16, n = 22, r12 = .70.

Test the following hypotheses at the .05 level of significance:

$\begin{array}{l}
H_{0}: \sigma_{1}^{2}-\sigma_{2}^{2}=0 \
H_{1}: \sigma_{1}^{2}-\sigma_{2}^{2} \neq 0
\end{array}$

Accepted Answer

The degrees of freedom (v) are equal to

Question 5

Which of the following are examples of types of research questions that can be answered with a test of inference about independent variances? Select all that apply.

Accepted Answer

A)  Does the variation in the time to complete a task different for subjects in a treatment group as compared to subjects in a control group? 
B)  Is variation in height different for children who drink the recommended number of glasses of water per day as compare to children who do not? 
C)  Is there a relationship between the variation of BMI in adults and weight in middle school? 
D)  Are there similar proportions of public institutions who declined in federal spending in 2000 as compared to 2010? 
A)  Does the variation in the time to complete a task different for subjects in a treatment group as compared to subjects in a control group? 
B)  Is variation in height different for children who drink the recommended number of glasses of water per day as compare to children who do not? 
C)  Is there a relationship between the variation of BMI in adults and weight in middle school? 
D)  Are there similar proportions of public institutions who declined in federal spending in 2000 as compared to 2010?

Question 6

A random sample of 51scores is collected with a sample mean of 75 and a sample variance of 10. Test the following hypotheses at the .05 level of significance:

$\begin{array}{l}
H_{0}: \sigma^{2}=7 \
H_{1}: \sigma^{2} \neq 7
\end{array}$

Accepted Answer

Degrees of freedom (S1U1B1vS1U1B0) are equal to S1U1B

Question 7

The following summary statistics are available for two dependent random samples:

s12 = 100, s22 = 225, n = 122, r12 = .50.

Test the following hypotheses at the .05 level of significance:

$\begin{array}{l}
H_{0}: \sigma_{1}^{2}-\sigma_{2}^{2}=0 \
H_{1}: \sigma_{1}^{2}-\sigma_{2}^{2} \neq 0
\end{array}$

Accepted Answer

The degrees of freedom (v) are equal to

Question 8

Which of the following are examples of types of research questions that can be answered with a test of inference about independent variances?

Accepted Answer

A)  Is there a relationship between book price and tuition? 
B)  Are there similar proportions of U.S. versus non-U.S. board graduates? 
C)  Is the variation in graduation rate for public colleges different than the graduation rate for private colleges? 
D)  Does weight vary for athletes who train 6 hours per day as compared to athlete who train 8 hours per day? 
E)  Is there a relationship between satisfaction with a job's salary and satisfaction with a job's level of responsibility?
F) Is there a mean difference in engagement in the workplace based on whether an employee is full-time or part-time? 
A)  Is there a relationship between book price and tuition? 
B)  Are there similar proportions of U.S. versus non-U.S. board graduates? 
C)  Is the variation in graduation rate for public colleges different than the graduation rate for private colleges? 
D)  Does weight vary for athletes who train 6 hours per day as compared to athlete who train 8 hours per day? 
E)  Is there a relationship between satisfaction with a job's salary and satisfaction with a job's level of responsibility?
F) Is there a mean difference in engagement in the workplace based on whether an employee is full-time or part-time?

A random sample of 5 scores is collected with a sample mean of 8 and a sample variance of 9. Test the following hypotheses at the .05 level of significance: :=5 :5

A random sample of 9 scores is collected with a sample mean of 62 and a sample variance of 16. Test the following hypotheses at the .05 level of significance: :=15 :15

In what is a researcher interested when conducting a test of inference for independent variances?

The following summary statistics are available for two dependent random samples: s₁² = 36, s₂² = 16, n = 22, r₁₂ = .70. Test the following hypotheses at the .05 level of significance: :-=0 :-0

Which of the following are examples of types of research questions that can be answered with a test of inference about independent variances? Select all that apply.

A random sample of 51scores is collected with a sample mean of 75 and a sample variance of 10. Test the following hypotheses at the .05 level of significance: :=7 :7

The following summary statistics are available for two dependent random samples: s₁² = 100, s₂² = 225, n = 122, r₁₂ = .50. Test the following hypotheses at the .05 level of significance: :-=0 :-0

Which of the following are examples of types of research questions that can be answered with a test of inference about independent variances?

Introduction

Data Representation

Univariate Population Parameters and Sample Statistics

The Normal Distribution and Standard Scores

Introduction to Probability and Sample Statistics

Introduction to Hypothesis Testing: Inferences About a Single Mean

Inferences About the Difference Between Two Means

Inferences About Proportions

Bivariate Measures of Association

One-Factor Anova: Fixed-Effects Mode

Multiple Comparison Procedures

Factorial Anova: Fixed-Effects Mode

One Factor Fixed-Effects Ancova With Single Covariate

Random- and Mixed-Effects Analysis of Variance Models

Hierarchical and Randomized Block Analysis of Variance Models

Simple Linear Regression

Multiple Linear Regression

Logistic Regression

Mediation and Moderation

Filters

Exam 9: Inferences About Variances

A random sample of 5 scores is collected with a sample mean of 8 and a sample variance of 9. Test the following hypotheses at the .05 level of significance: :=5 :5

A random sample of 9 scores is collected with a sample mean of 62 and a sample variance of 16. Test the following hypotheses at the .05 level of significance: :=15 :15

In what is a researcher interested when conducting a test of inference for independent variances?

The following summary statistics are available for two dependent random samples: s12 = 36, s22 = 16, n = 22, r12 = .70. Test the following hypotheses at the .05 level of significance: :-=0 :-0

Which of the following are examples of types of research questions that can be answered with a test of inference about independent variances? Select all that apply.

A random sample of 51scores is collected with a sample mean of 75 and a sample variance of 10. Test the following hypotheses at the .05 level of significance: :=7 :7

The following summary statistics are available for two dependent random samples: s12 = 100, s22 = 225, n = 122, r12 = .50. Test the following hypotheses at the .05 level of significance: :-=0 :-0

Which of the following are examples of types of research questions that can be answered with a test of inference about independent variances?

Introduction

Data Representation

Univariate Population Parameters and Sample Statistics

The Normal Distribution and Standard Scores

Introduction to Probability and Sample Statistics

Introduction to Hypothesis Testing: Inferences About a Single Mean

Inferences About the Difference Between Two Means

Inferences About Proportions

Bivariate Measures of Association

One-Factor Anova: Fixed-Effects Mode

Multiple Comparison Procedures

Factorial Anova: Fixed-Effects Mode

One Factor Fixed-Effects Ancova With Single Covariate

Random- and Mixed-Effects Analysis of Variance Models

Hierarchical and Randomized Block Analysis of Variance Models

Simple Linear Regression

Multiple Linear Regression

Logistic Regression

Mediation and Moderation

Filters

The following summary statistics are available for two dependent random samples: s₁² = 36, s₂² = 16, n = 22, r₁₂ = .70. Test the following hypotheses at the .05 level of significance: :-=0 :-0

The following summary statistics are available for two dependent random samples: s₁² = 100, s₂² = 225, n = 122, r₁₂ = .50. Test the following hypotheses at the .05 level of significance: :-=0 :-0