Question 1

In single-factor ANOVA, the __________ is a measure of between samples variation, and is denoted by __________.

Accepted Answer

mean square for treatments, MSTr

Question 2

In a one-way ANOVA problem involving four populations or treatments, the null hypothesis of interest is $H _ { 0 } :$$\underline{\quad\quad}$

Accepted Answer

$\mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 } = \mu _ { 4 }$

Question 3

In one-factor ANOVA, __________ denoted by __________ is the part of total variation that can be explained by possible differences in the population means.

Accepted Answer

sum square for treatments, SSTr

Question 4

Which of the following statements are not true?

Accepted Answer

A)  ANOVA can be used to test $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \text { versus } H _ { \pm } : \mu _ { 1 } \neq \mu _ { 2 }$
) 
B)  ANOVA cannot be used to test $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \text { versus } H _ { \pm } : \mu _ { 1 } \neq \mu _ { 2 }$
) 
C)  ANOVA can be used to test $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 } \text { versus } H _ { \pm } :$
At least two of the $\mu _ { i } ^ { \prime } s$
Are different. 
D)  The two-sample t test can be used to test $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \text { versus } H _ { \pm } : \mu _ { 1 } \neq \mu _ { 2 }$
) 
E)  All of the above statements are true. 
A)  ANOVA can be used to test $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \text { versus } H _ { \pm } : \mu _ { 1 } \neq \mu _ { 2 }$
) 
B)  ANOVA cannot be used to test $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \text { versus } H _ { \pm } : \mu _ { 1 } \neq \mu _ { 2 }$
) 
C)  ANOVA can be used to test $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 } \text { versus } H _ { \pm } :$
At least two of the $\mu _ { i } ^ { \prime } s$
Are different. 
D)  The two-sample t test can be used to test $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \text { versus } H _ { \pm } : \mu _ { 1 } \neq \mu _ { 2 }$
) 
E)  All of the above statements are true.

Question 5

In single-factor ANOVA, MSTr is the mean square for treatments, and MSE is the mean square for error. Which of the following statements are not true?

Accepted Answer

A)  MSE is a measure of between-samples variation. 
B)  MSE is a measure of within-samples variation. 
C)  MSTr is a measure of between-samples variation. 
D)  The value of MSTr is affected by the status of $H _ { o }$
(true or false). 
E)  All of the above statements are true 
A)  MSE is a measure of between-samples variation. 
B)  MSE is a measure of within-samples variation. 
C)  MSTr is a measure of between-samples variation. 
D)  The value of MSTr is affected by the status of $H _ { o }$
(true or false). 
E)  All of the above statements are true

Question 6

In one-way ANOVA, which of the following statements are true?

Accepted Answer

A)  SST is a measure of the total variation in the data. 
B)  SSE measures variation that would be present within treatments even if $H _ { o }$
Were true, and is thus the part of total variation that is unexplained by the truth or falsity of $H _ { o }$
) 
C)  SSTr is the amount of variation between treatments that can be explained by possible differences in the population or treatments' means. 
D)  If explained variation is large relative to unexplained variation, then $H _ { o }$
Is rejected in favor of $H _ { \pm }$
) 
E)  All of the above statements are true. 
A)  SST is a measure of the total variation in the data. 
B)  SSE measures variation that would be present within treatments even if $H _ { o }$
Were true, and is thus the part of total variation that is unexplained by the truth or falsity of $H _ { o }$
) 
C)  SSTr is the amount of variation between treatments that can be explained by possible differences in the population or treatments' means. 
D)  If explained variation is large relative to unexplained variation, then $H _ { o }$
Is rejected in favor of $H _ { \pm }$
) 
E)  All of the above statements are true.

Question 7

Folacin is the only B vitamin present in any significant amount in tea, and recent advances in assay methods have made accurate determination of folacin content feasible. Consider the accompanying data on folacin content for randomly selected specimens of the four leading brands of green tea. Brand Observations $\begin{array} { l | l l l l l l l } 
\hline 1 & 8.0 & 6.3 & 6.7 & 8.7 & 9.0 & 10.2 & 9.7 \
2 & 5.8 & 7.6 & 9.9 & 6.2 & 8.5 & & \
3 & 6.9 & 7.6 & 5.1 & 7.5 & 5.4 & 6.2 & \
4 & 6.5 & 7.2 & 8.0 & 4.6 & 5.1 & 4.1 & \
\hline
\end{array}$ Does this data suggest that true average folacin content is the same for all brands?

Accepted Answer

A)  Carry out a test using $$\alpha = .05$$
Via the P-value method. 
B)  Perform a multiple comparisons analysis to identify significant differences among brands. 
A)  Carry out a test using $$\alpha = .05$$
Via the P-value method. 
B)  Perform a multiple comparisons analysis to identify significant differences among brands.

Question 8

Let F =MSTr/MSE be the test statistic in a single-factor ANOVA problem involving four populations or treatments with a random sample of six observations from each one. When $H _ { o }$ is true and the four population or treatment distributions are all normal with the same variance $\sigma ^ { 2 }$ then F has an F distribution with degrees of freedom $v _ { 1 } =$$\underline{\quad\quad}$and $v _ { 2 } =$$\underline{\quad\quad}$ With f denoting the computed value of F, the rejection region for level .05 test is __________.

Accepted Answer

The answer of Let F =MSTr/MSE be the test statistic...

Question 9

In a single-factor ANOVA problem involving 5 populations, assume that the sample sizes from each population are not equal, and that the total number of observations is 21. If SSTr = 8 and SST = 12, then MSTr = __________, MSE = __________, and the test statistic value f = __________.

Accepted Answer

The answer of In a single-factor ANOVA problem involving 5...

Question 10

In a single-factor ANOVA problem involving 4 populations, the sample sizes are 7,5,6, and 6. If SST = 65.27 and SSTr = 23.49, then the test statistic value f is

Accepted Answer

A)  3.75 
B)  2.09 
C)  7.83 
D)  0.56 
E)  6.67 
A)  3.75 
B)  2.09 
C)  7.83 
D)  0.56 
E)  6.67

Question 11

In a single-factor ANOVA, the characteristic that differentiates the treatments or populations from one another is called the __________ under study, and the different treatments or populations are referred to as the __________ of the factor.

Accepted Answer

The answer of In a single-factor ANOVA, the characteristic that...

Question 12

In single-factor ANOVA, the __________ is a measure of within-samples variation, and is denoted by __________.

Accepted Answer

mean squar

Question 13

In a single-factor ANOVA problem involving five populations or treatments, which of the following statements are true about the alternative hypothesis?

Accepted Answer

A)  All five population means are equal. 
B)  All five population means are different. 
C)  At least two of the population mean are different. 
D)  At least three of the population mean are different. 
E)  At most, two of the population means are equal. 
A)  All five population means are equal. 
B)  All five population means are different. 
C)  At least two of the population mean are different. 
D)  At least three of the population mean are different. 
E)  At most, two of the population means are equal.

Question 14

Define a parameter $\mu$ by $\mu = \sum _ { i = 1 } ^ { J } \mu _ { i } / I$ and the parameters $\alpha _ { 1 } , \ldots \ldots \ldots , \alpha _ { j }$ by $\alpha _ { i } = \mu _ { i} - \mu$ . Then, $\sum _ { i = 1 } ^ { 3 } \alpha _ { i } =$ __________.

Accepted Answer

The answer of Define a parameter $\mu$ by \(\mu =...

Question 15

Consider calculating a 95% confidence interval for a population mean $\mu$ based on a sample from a population, and then a 95% confidence interval for a population proportion p based on another sample selected independently from the same population. Which of the following statements are true?

Accepted Answer

A)  Prior to obtaining data, the probability that the first interval will include $\mu$
Is )95. 
B)  Prior to obtaining data, the probability that the second interval will include p is .95. 
C)  The probability that both intervals will include the values of the respective parameters is about .90. 
D)  All of the above statements are correct. 
A)  Prior to obtaining data, the probability that the first interval will include $\mu$
Is )95. 
B)  Prior to obtaining data, the probability that the second interval will include p is .95. 
C)  The probability that both intervals will include the values of the respective parameters is about .90. 
D)  All of the above statements are correct.

Question 16

The assumptions of single-factor ANOVA can be described succinctly by means of the "model equation" $X _ {ij } = \mu _ { i } + \varepsilon _ {  ij } \text { where } \varepsilon _ { ij }$ represents a random deviation from the population or true treatment mean $\mu _ { i }$ . Which of the following statements are true?

Accepted Answer

A)  The $\varepsilon _ {ij } ^ { \prime } \mathrm { s }$
Are assumed to be independent. 
B)  The $\varepsilon _ { i j } ^ { \prime } \mathrm { s }$
Are normally distributed random variables. 
C)  $E \left( \varepsilon _ { ij } \right) = 0$
For every i and j. 
D)  $V \left( \varepsilon _ {ij } \right) = \sigma ^ { 2 }$
For every i and j. 
E)  All of the above statements are true. 
A)  The $\varepsilon _ {ij } ^ { \prime } \mathrm { s }$
Are assumed to be independent. 
B)  The $\varepsilon _ { i j } ^ { \prime } \mathrm { s }$
Are normally distributed random variables. 
C)  $E \left( \varepsilon _ { ij } \right) = 0$
For every i and j. 
D)  $V \left( \varepsilon _ {ij } \right) = \sigma ^ { 2 }$
For every i and j. 
E)  All of the above statements are true.

Question 17

In single-factor ANOVA, MSE is the mean square for error, and MSTr is the mean square for treatments. Which of the following statements are not true?

Accepted Answer

A)  The value of MSTr is affected by the status of $H _ { o }$
(true or false) 
B)  When $H _ { o }$
Is true, E(MSTr) = E(MS
E)  = $\sigma ^ { 2 } \text { where } \sigma ^ { 2 }$
Is the common population variance. 
C)  When $H _ { o }$
Is false, E(MSTr) > E(MS
E)  = $\sigma ^ { 2 } \text { where } \sigma ^ { 2 }$
Is the common population variance. 
D)  The value of MSE is affected by the status of $H _ { o }$
(true or false). 
E)  All of the above statements are true. 
A)  The value of MSTr is affected by the status of $H _ { o }$
(true or false) 
B)  When $H _ { o }$
Is true, E(MSTr) = E(MS
E)  = $\sigma ^ { 2 } \text { where } \sigma ^ { 2 }$
Is the common population variance. 
C)  When $H _ { o }$
Is false, E(MSTr) > E(MS
E)  = $\sigma ^ { 2 } \text { where } \sigma ^ { 2 }$
Is the common population variance. 
D)  The value of MSE is affected by the status of $H _ { o }$
(true or false). 
E)  All of the above statements are true.

Question 18

In a single-factor ANOVA problem involving 3 treatments, the sample means were 5,6, and 9. If each observation in the third sample was increased by 20, the test statistic value f would

Accepted Answer

A)  increase 
B)  decrease 
C)  remain the same 
D)  increase by 20 
E)  decrease by 10 
A)  increase 
B)  decrease 
C)  remain the same 
D)  increase by 20 
E)  decrease by 10

Question 19

__________ multiple comparisons procedure involves the use of probability distributed called the Studentized range distribution.

Accepted Answer

The answer of __________ multiple comparisons procedure involves the use...

Question 20

In a single-factor ANOVA problem involving four populations or treatments, the four sample standard deviations are 25.6, 30.4, 28.7, and 32.50. Then, the mean square for error is

Accepted Answer

A)  29.3 
B)  117.2 
C)  864.865 
D)  29.409 
E)  None of the above answers are correct. 
A)  29.3 
B)  117.2 
C)  864.865 
D)  29.409 
E)  None of the above answers are correct.

In single-factor ANOVA, the is a measure of between samples variation, and is denoted by .

In a one-way ANOVA problem involving four populations or treatments, the null hypothesis of interest is $H _ { 0 } :$ $\underline{\quad\quad}$

In one-factor ANOVA, denoted by is the part of total variation that can be explained by possible differences in the population means.

Which of the following statements are not true?

In single-factor ANOVA, MSTr is the mean square for treatments, and MSE is the mean square for error. Which of the following statements are not true?

In one-way ANOVA, which of the following statements are true?

In a single-factor ANOVA problem involving 5 populations, assume that the sample sizes from each population are not equal, and that the total number of observations is 21. If SSTr = 8 and SST = 12, then MSTr = , MSE = , and the test statistic value f = __.

In a single-factor ANOVA problem involving 4 populations, the sample sizes are 7,5,6, and 6. If SST = 65.27 and SSTr = 23.49, then the test statistic value f is

In a single-factor ANOVA, the characteristic that differentiates the treatments or populations from one another is called the under study, and the different treatments or populations are referred to as the of the factor.

In single-factor ANOVA, the is a measure of within-samples variation, and is denoted by .

In a single-factor ANOVA problem involving five populations or treatments, which of the following statements are true about the alternative hypothesis?

Define a parameter $\mu$ by $\mu = \sum _ { i = 1 } ^ { J } \mu _ { i } / I$ and the parameters $\alpha _ { 1 } , \ldots \ldots \ldots , \alpha _ { j }$ by $\alpha _ { i } = \mu _ { i} - \mu$ . Then, $\sum _ { i = 1 } ^ { 3 } \alpha _ { i } =$ __________.

Consider calculating a 95% confidence interval for a population mean $\mu$ based on a sample from a population, and then a 95% confidence interval for a population proportion p based on another sample selected independently from the same population. Which of the following statements are true?

In single-factor ANOVA, MSE is the mean square for error, and MSTr is the mean square for treatments. Which of the following statements are not true?

In a single-factor ANOVA problem involving 3 treatments, the sample means were 5,6, and 9. If each observation in the third sample was increased by 20, the test statistic value f would

__________ multiple comparisons procedure involves the use of probability distributed called the Studentized range distribution.

In a single-factor ANOVA problem involving four populations or treatments, the four sample standard deviations are 25.6, 30.4, 28.7, and 32.50. Then, the mean square for error is

Overview and Descriptive Statistics

Probability

Discrete Random Variables and Probability Distributions

Continuous Random Variables and Probability Distributions

Joint Probability Distributions and Random Samples

Point Estimation

Statistical Intervals Based on a Single Sample

Tests of Hypotheses Based on a Single Sample

Inferences Based on Two Samples

Multifactor Analysis of Variance

Simple Linear Regression and Correlation

Nonlinear and Multiple Regression

Goodness-Of-Fit Tests and Categorical Data Analysis

Distribution-Free Procedures

Quality Control Methods

Filters

Exam 10: The Analysis of Variance

In single-factor ANOVA, the __________ is a measure of between samples variation, and is denoted by __________.

In a one-way ANOVA problem involving four populations or treatments, the null hypothesis of interest is H0:H _ { 0 } :H0​:‾\underline{\quad\quad}​

In one-factor ANOVA, __________ denoted by __________ is the part of total variation that can be explained by possible differences in the population means.

Which of the following statements are not true?

In single-factor ANOVA, MSTr is the mean square for treatments, and MSE is the mean square for error. Which of the following statements are not true?

In one-way ANOVA, which of the following statements are true?

In a single-factor ANOVA problem involving 5 populations, assume that the sample sizes from each population are not equal, and that the total number of observations is 21. If SSTr = 8 and SST = 12, then MSTr = __________, MSE = __________, and the test statistic value f = __________.

In a single-factor ANOVA problem involving 4 populations, the sample sizes are 7,5,6, and 6. If SST = 65.27 and SSTr = 23.49, then the test statistic value f is

In a single-factor ANOVA, the characteristic that differentiates the treatments or populations from one another is called the __________ under study, and the different treatments or populations are referred to as the __________ of the factor.

In single-factor ANOVA, the __________ is a measure of within-samples variation, and is denoted by __________.

In a single-factor ANOVA problem involving five populations or treatments, which of the following statements are true about the alternative hypothesis?

Consider calculating a 95% confidence interval for a population mean μ\muμ based on a sample from a population, and then a 95% confidence interval for a population proportion p based on another sample selected independently from the same population. Which of the following statements are true?

In single-factor ANOVA, MSE is the mean square for error, and MSTr is the mean square for treatments. Which of the following statements are not true?

In a single-factor ANOVA problem involving 3 treatments, the sample means were 5,6, and 9. If each observation in the third sample was increased by 20, the test statistic value f would

__________ multiple comparisons procedure involves the use of probability distributed called the Studentized range distribution.

In a single-factor ANOVA problem involving four populations or treatments, the four sample standard deviations are 25.6, 30.4, 28.7, and 32.50. Then, the mean square for error is

Overview and Descriptive Statistics

Probability

Discrete Random Variables and Probability Distributions

Continuous Random Variables and Probability Distributions

Joint Probability Distributions and Random Samples

Point Estimation

Statistical Intervals Based on a Single Sample

Tests of Hypotheses Based on a Single Sample

Inferences Based on Two Samples

Multifactor Analysis of Variance

Simple Linear Regression and Correlation

Nonlinear and Multiple Regression

Goodness-Of-Fit Tests and Categorical Data Analysis

Distribution-Free Procedures

Quality Control Methods

Filters

In single-factor ANOVA, the is a measure of between samples variation, and is denoted by .

In a one-way ANOVA problem involving four populations or treatments, the null hypothesis of interest is $H _ { 0 } :$ $\underline{\quad\quad}$

In one-factor ANOVA, denoted by is the part of total variation that can be explained by possible differences in the population means.

In a single-factor ANOVA problem involving 5 populations, assume that the sample sizes from each population are not equal, and that the total number of observations is 21. If SSTr = 8 and SST = 12, then MSTr = , MSE = , and the test statistic value f = __.

In a single-factor ANOVA, the characteristic that differentiates the treatments or populations from one another is called the under study, and the different treatments or populations are referred to as the of the factor.

In single-factor ANOVA, the is a measure of within-samples variation, and is denoted by .

Consider calculating a 95% confidence interval for a population mean $\mu$ based on a sample from a population, and then a 95% confidence interval for a population proportion p based on another sample selected independently from the same population. Which of the following statements are true?