Question 1

Fill in the missing entries in the following partially completed one -way ANOVA table. $$\begin{array} { l | c | c | c | c } 
\text { Source } & d \boldsymbol { f } & \boldsymbol { S S } & \boldsymbol { M S } = \boldsymbol { S S } / d f & \boldsymbol { F } \text {-statistic } \
\hline \text { Treatment } & 3 & & & 11.16 \
\hline \text { Error } & & 13.72 & 0.686 &
\end{array}$$

Accepted Answer

A) $$\begin{array} { l | c | c | c | c } 
\text { Source } & \boldsymbol { d f } & \boldsymbol { S S } & \boldsymbol { M S } = \boldsymbol { S S } / d \boldsymbol { f } & \boldsymbol { F } \text {-statistic } \
\hline \text { Treatment } & 3 & 22.97 & 7.66 & 11.16 \
\hline \text { Error } & 20 & 13.72 & 0.686 & \
\hline \text { Total } & 23 & 36.69 & &
\end{array}$$ 
B) $$\begin{array} { l | c | c | c | c } 
\text { Source } & d \boldsymbol { f } & \boldsymbol { S S } & \boldsymbol { M S } = \boldsymbol { S S } / d f & \boldsymbol { F } \text {-statistic } \
\hline \text { Treatment } & 3 & 2.55 & 7.66 & 11.16 \
\hline \text { Error } & 20 & 13.72 & 0.686 & \
\hline \text { Total } & 23 & 16.27 & &
\end{array}$$ 
C) $$\begin{array} { l | c | c | c | c } 
\text { Source } & d f & \boldsymbol { S S } & \boldsymbol { M S } = \boldsymbol { S S } / d \boldsymbol { d } & \boldsymbol { F } \text {-statistic } \
\hline \text { Treatment } & 3 & 48.80 & 16.27 & 11.16 \
\hline \text { Error } & 20 & 13.72 & 0.686 & \
\hline \text { Total } & 23 & 62.52 & &
\end{array}$$ 
D) $$\begin{array} { l | c | c | c | c } 
\text { Source } & \boldsymbol { d f } & \boldsymbol { S S } & \boldsymbol { M S } = \boldsymbol { S S } / \boldsymbol { d f } & \boldsymbol { F } \text {-statistic } \
\hline \text { Treatment } & 3 & 0.184 & 0.061 & 11.16 \
\hline \text { Error } & 20 & 13.72 & 0.686 & \
\hline \text { Total } & 23 & 13.90 & &
\end{array}$$ 
A) $$\begin{array} { l | c | c | c | c } 
\text { Source } & \boldsymbol { d f } & \boldsymbol { S S } & \boldsymbol { M S } = \boldsymbol { S S } / d \boldsymbol { f } & \boldsymbol { F } \text {-statistic } \
\hline \text { Treatment } & 3 & 22.97 & 7.66 & 11.16 \
\hline \text { Error } & 20 & 13.72 & 0.686 & \
\hline \text { Total } & 23 & 36.69 & &
\end{array}$$ 
B) $$\begin{array} { l | c | c | c | c } 
\text { Source } & d \boldsymbol { f } & \boldsymbol { S S } & \boldsymbol { M S } = \boldsymbol { S S } / d f & \boldsymbol { F } \text {-statistic } \
\hline \text { Treatment } & 3 & 2.55 & 7.66 & 11.16 \
\hline \text { Error } & 20 & 13.72 & 0.686 & \
\hline \text { Total } & 23 & 16.27 & &
\end{array}$$ 
C) $$\begin{array} { l | c | c | c | c } 
\text { Source } & d f & \boldsymbol { S S } & \boldsymbol { M S } = \boldsymbol { S S } / d \boldsymbol { d } & \boldsymbol { F } \text {-statistic } \
\hline \text { Treatment } & 3 & 48.80 & 16.27 & 11.16 \
\hline \text { Error } & 20 & 13.72 & 0.686 & \
\hline \text { Total } & 23 & 62.52 & &
\end{array}$$ 
D) $$\begin{array} { l | c | c | c | c } 
\text { Source } & \boldsymbol { d f } & \boldsymbol { S S } & \boldsymbol { M S } = \boldsymbol { S S } / \boldsymbol { d f } & \boldsymbol { F } \text {-statistic } \
\hline \text { Treatment } & 3 & 0.184 & 0.061 & 11.16 \
\hline \text { Error } & 20 & 13.72 & 0.686 & \
\hline \text { Total } & 23 & 13.90 & &
\end{array}$$

Question 2

Identify the value of the test statistic. $$\begin{array} { l | r | c | c | c | c } 
\text { Source } & \boldsymbol { D } \boldsymbol { F } & \boldsymbol { S S } & \boldsymbol { M S } & \boldsymbol { F } & \boldsymbol { p } \
\hline \text { Factor } & 3 & 30 & 10.00 & 1.6 & 0.264 \
\hline \text { Error } & 8 & 50 & 6.25 & & \
\hline \text { Total } & 11 & 80 & & &
\end{array}$$

Accepted Answer

A)  30 
B)   1.6 
C)   0.264 
D)   10.00 
A)  30 
B)   1.6 
C)   0.264 
D)   10.00

Question 3

Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance. $\begin{array} { c c c } 
\text { Exercise A } & \text { Exercise B } & \text { Exercise } \mathbf { C } \
\hline 2.5 & 5.8 & 4.3 \
8.8 & 4.9 & 6.2 \
7.3 & 1.1 & 5.8 \
9.8 & 7.8 & 8.1 \
5.1 & 1.2 & 7.9
\end{array}$
 At the 1% significance level, does it appear that a difference exists in the true mean weight loss produced by the three exercise programs?

Accepted Answer

Test statistic: F = 1.491. Critical valu

Question 4

Given below are the analysis of variance results from a Minitab display. to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. Identify the P-value. $$\begin{array} { l | r | c | l | c | c } 
\text { Source } & \boldsymbol { D F } & \boldsymbol { S S } & \boldsymbol { M S } & \boldsymbol { F } & \boldsymbol { p } \
\hline \text { Factor } & 3 & 13.500 & 4.500 & 5.17 & 0.011 \
\hline \text { Error } & 16 & 13.925 & 0.870 & & \
\hline \text { Total } & 19 & 27.425 & & &
\end{array}$$

Accepted Answer

A)   4.500 
B)   5.17 
C)   0.870 
D)   0.011 
A)   4.500 
B)   5.17 
C)   0.870 
D)   0.011

Question 5

Which of the following is NOT a requirement for one-way ANOVA?

Accepted Answer

A)  The populations have distributions that are approximately normal. 
B)  The samples are simple random samples. 
C)  The samples are independent of each other. 
D)  The data is categorical data. 
A)  The populations have distributions that are approximately normal. 
B)  The samples are simple random samples. 
C)  The samples are independent of each other. 
D)  The data is categorical data.

Question 6

Given below are the analysis of variance results from a Minitab display. to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. What can you conclude about the equality of the
Population means? $$\begin{array} { l | r | c | c | c | c } 
\text { Source } & \boldsymbol { D } \boldsymbol { F } & \boldsymbol { S S } & \boldsymbol { M S } & \boldsymbol { F } & \boldsymbol { p } \
\hline \text { Factor } & 3 & 13.500 & 4.500 & 5.17 & 0.011 \
\hline \text { Error } & 16 & 13.925 & 0.870 & & \
\hline \text { Total } & 19 & 27.425 & & &
\end{array}$$

Accepted Answer

A)  Reject the null hypothesis since the P-value is greater than the significance level. 
B)  Accept the null hypothesis since the P-value is less than the significance level. 
C)  Accept the null hypothesis since the P-value is greater than the significance level. 
D)  Reject the null hypothesis since the P-value is less than the significance level. 
A)  Reject the null hypothesis since the P-value is greater than the significance level. 
B)  Accept the null hypothesis since the P-value is less than the significance level. 
C)  Accept the null hypothesis since the P-value is greater than the significance level. 
D)  Reject the null hypothesis since the P-value is less than the significance level.

Question 7

Explain the procedure for two-way analysis of variance, and how it varies depending on whether there is an interaction between the two factors or not.

Accepted Answer

First we test whether there is an effect

Question 8

Given below are the analysis of variance results from a Minitab display. to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. Identify the value of the test statistic. $$\begin{array} { l | r | c | c | c | c } 
\text { Source } & \boldsymbol { D F } & \boldsymbol { S S } & \boldsymbol { M S } & \boldsymbol { F } & \boldsymbol { p } \
\hline \text { Factor } & 3 & 13.500 & 4.500 & 5.17 & 0.011 \
\hline \text { Error } & 16 & 13.925 & 0.870 & & \
\hline \text { Total } & 19 & 27.425 & & &
\end{array}$$

Accepted Answer

A)   5.17 
B)   4.500 
C)   13.500 
D)   0.011 
A)   5.17 
B)   4.500 
C)   13.500 
D)   0.011

Question 9

The data below represent the weight losses for people on three diets
 $\begin{array} { l c c } 
\text { Diet A } & \text { Diet B } & \text { Diet C } \
\hline 1.75 & 3.8 & 4.8 \
8.8 & 4.9 & 6.2 \
7.3 & 1.1 & 5.8 \
9.8 & 7.8 & 8.1 \
5.1 & 1.2 & 6.9
\end{array}$ 
If we want to test the claim that the three size categories have the same means, why don't we use three separate hypothesis tests for $\mu _ { 1 } = \mu _ { 2 } , \mu _ { 2 } = \mu _ { 3 } , \text { and } \mu _ { 1 } = \mu _ { 3 } ?$

Accepted Answer

As we increase the number of i

Question 10

ANOVA requires usage of the _______ distribution

Accepted Answer

A)  Normal 
B)  t 
C)  Chi-square 
D)  F 
A)  Normal 
B)  t 
C)  Chi-square 
D)  F

Question 11

The following data contains task completion times, in minutes, categorized according to the gender of the machine operator and the machine used.

The ANOVA results lead us to conclude that the completion times are not affected by an interaction between machine and gender, and the times are not affected by gender, but they are affected by the machine. Change the table entries so that there is an effect from the interaction between machine and gender.

Accepted Answer

The following table is one exa

Question 12

Assume that the number of items produced is not affected by an interaction between employee and machine. Using a 0.05 significance level, test the claim that the machine has no effect on
the number of items produced.   Using a 0.05 significance level, test the claim that the interaction between employee and
machine has no effect on the number of items produced.

Accepted Answer

H₀ : There is no interaction effect. H

Question 13

Draw an example of an F distribution and list the characteristics of the F distribution

Accepted Answer

1) The  F  distribution is not symmetric

Question 14

The following data contains task completion times, in minutes, categorized according to the gender of the machine operator and the machine used.
$\begin{array} { l c c } 
& \text { Male } & \text { Female } \
\text { Machine 1 } & 15,17 & 16,17 \
\text { Machine 2 } & 14,13 & 15,13 \
\text { Machine 3 } & 16,18 & 17,19
\end{array}$
The ANOVA results lead us to conclude that the completion times are not affected by an interaction between machine and gender, and the times are not affected by gender, but they are affected by the machine. Change the table entries so that there is no effect from the interaction between machine and gender, but there is an effect from the gender of the operator.

Accepted Answer

The following table is one example of en

Question 15

Select a property of the F distribution

Accepted Answer

A)  It is symmetric. 
B)  The exact shape of the F distribution depends on two different degrees of freedom. 
C)  Values of the F distribution can be negative. 
D)  The total area under the curve is equal to 2. 
A)  It is symmetric. 
B)  The exact shape of the F distribution depends on two different degrees of freedom. 
C)  Values of the F distribution can be negative. 
D)  The total area under the curve is equal to 2.

Question 16

Select an appropriate null hypothesis for a one way analysis of variance test.

Accepted Answer

A)   H0: $\mu$1 = $\mu$2 = $\mu$3 = $\mu$4 
B)   H0: $\mu$1 ≠ $\mu$2 ≠ $\mu$3 ≠ $\mu$4 
C)   H0: p1 ≠ p2 ≠ p3 ≠ p4 
D)  H0 : σ1 = σ2 = σ3 = σ4 
A)   H0: $\mu$1 = $\mu$2 = $\mu$3 = $\mu$4 
B)   H0: $\mu$1 ≠ $\mu$2 ≠ $\mu$3 ≠ $\mu$4 
C)   H0: p1 ≠ p2 ≠ p3 ≠ p4 
D)  H0 : σ1 = σ2 = σ3 = σ4

Question 17

Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance. At the 0.025 significance level, test the claim that the four brands have the same mean if the following sample results havebeen obtained. $\begin{array} { c c c c } 
\text { Brand A } & \text { Brand B } & \text { Brand C } & \text { Brand D } \
\hline 17 & 18 & 21 & 22 \
20 & 18 & 24 & 25 \
21 & 23 & 25 & 27 \
22 & 25 & 26 & 29 \
21 & 26 & 29 & 35 \
& & 29 & 36 \
& & & 37
\end{array}$

Accepted Answer

@#LAT-DLM&₀ = @#LAT-DLM&₁ = @#LAT-DLM&₂

Question 18

The following data shows the yield, in bushels per acre, categorized according to three varieties of corn and three different soil conditions. Assume that yields are not affected by an interaction between variety and soil conditions, and test the null hypothesis that variety has no effect on yield. Use a 0.05 significance level.
 $\begin{array} { c | c c c } 
& \text { Plot 1 } & \text { Plot 2 } & \text { Plot 3 } \
\hline \text { Variety 1 } & 156,167 , & 162,160 , & 145,151 , \
& 170,162 & 169,168 & 148,155 \
\text { Variety 2 } & 172,176 , & 179,186 , & 161,162 , \
& 166,179 & 160,176 & 165,170 \
\text { Variety 3 } & 175,157 , & 178,170 , & 169,165 , \
& 179,178 & 172,174 & 170,169
\end{array}$

Accepted Answer

H₀: Variety has no effect on yield. H₁

Question 19

Fill in the missing entries in the following partially completed one-way ANOVA table 
$\begin{array} { l | l | l | l | l } 
\text { Source } & \boldsymbol { d f } & \boldsymbol { S S } & \boldsymbol { M S } & \boldsymbol { F } \
\hline \text { Treatment } & 3 & & & 13.89 \
\hline \text { Error } & & 13.58 & 0.617 & \
\hline \text { Total } & & & &
\end{array}$

Accepted Answer

None

Question 20

At the same time each day, a researcher records the temperature in each of three greenhouses. The table shows the temperatures in degrees Fahrenheit recorded for one week.
 
i) Use a  0.05  significance level to test the claim that the average temperature is the same in each greenhouse.
ii) How are the analysis of variance results affected if the same constant is added to every one of the original sample values?

Accepted Answer

i) Reject the claim that the a

Fill in the missing entries in the following partially completed one -way ANOVA table. Source d = /df -statistic Treatment 3 11.16 Error 13.72 0.686

Identify the value of the test statistic. Source Factor 3 30 10.00 1.6 0.264 Error 8 50 6.25 Total 11 80

Which of the following is NOT a requirement for one-way ANOVA?

Explain the procedure for two-way analysis of variance, and how it varies depending on whether there is an interaction between the two factors or not.

ANOVA requires usage of the _______ distribution

Draw an example of an F distribution and list the characteristics of the F distribution

Select a property of the F distribution

Select an appropriate null hypothesis for a one way analysis of variance test.

Fill in the missing entries in the following partially completed one-way ANOVA table Source Treatment 3 13.89 Error 13.58 0.617 Total

Introduction to Statistics

Exploring Data With Tables and Graphs

Describing, Exploring, and Comparing Data

Probability

Discrete Probability Distributions

Normal Probability Distributions

Estimating Parameters and Determining Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Goodness-Of-Fit and Contingency Tables

Nonparametric Tests

Statistical Process Control

Filters

Exam 12: Analysis of Variance

Fill in the missing entries in the following partially completed one -way ANOVA table. Source d = /df -statistic Treatment 3 11.16 Error 13.72 0.686

Identify the value of the test statistic. Source Factor 3 30 10.00 1.6 0.264 Error 8 50 6.25 Total 11 80

Which of the following is NOT a requirement for one-way ANOVA?

Explain the procedure for two-way analysis of variance, and how it varies depending on whether there is an interaction between the two factors or not.

ANOVA requires usage of the _______ distribution

Draw an example of an F distribution and list the characteristics of the F distribution

Select a property of the F distribution

Select an appropriate null hypothesis for a one way analysis of variance test.

Fill in the missing entries in the following partially completed one-way ANOVA table Source Treatment 3 13.89 Error 13.58 0.617 Total

Introduction to Statistics

Exploring Data With Tables and Graphs

Describing, Exploring, and Comparing Data

Probability

Discrete Probability Distributions

Normal Probability Distributions

Estimating Parameters and Determining Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Goodness-Of-Fit and Contingency Tables

Nonparametric Tests

Statistical Process Control

Filters