Question 1

__________ is a particular combination of levels of the factors involved in a study.

Accepted Answer

A)  The factor level 
B)  The sampling design 
C)  An analysis of variance 
D)  A treatment 
A)  The factor level 
B)  The sampling design 
C)  An analysis of variance 
D)  A treatment

Question 2

A partially completed ANOVA table for a completely randomized design is shown here. $$\begin{array} { l c c c c } 
\text { Source } & \text { df } & \text { SS } & \text { MS } & F \
\hline \text { Time } & & 25.2 & \
\text { Error } & 11 & & \
\hline \text { Total } & 13 & 86.4 & \
\hline
\end{array}$$ a. Complete the ANOVA table.
b. How many treatments are involved in the experiment?
c. Do the data provide sufficient evidence to indicate a difference among the population means? Test using $\alpha = .05$

Accepted Answer

None

Question 3

307 diamonds were sampled and randomly sorted into three groups of diamonds. These diamonds were randomly assigned to one of the three organizations, or groups (HRD, GIA, or IGI), that certify the appraisal of diamonds. A study was conducted to determine if the average size of
Diamonds reported by these three certification groups differ. A completely randomized design was used and the resulting ANOVA table is shown below.

One-Way AOV for CARAT by CERT
$\begin{array}{lccccc}
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\hline \text { CERT } & 2 & 8.3265 & 4.16326 & 83.21 & 0.0000 \
\text { Error } & 305 & 15.2604 & 0.05003 & &
\end{array}$

Give a practical conclusion for the test in the words of the problem. Use $\alpha = 0.10$ to make your conclusion.

Accepted Answer

A)  There is sufficient evidence to indicate that differences exist among the mean carat weights for the three certification groups. 
B)  There is sufficient evidence to indicate that the mean carat weight for the HRD group equals the mean carat weight for the IGI group. 
C)  There is sufficient evidence to indicate that the mean carat weight for the GIA group is lower than the other two groups. 
D)  There is insufficient evidence to indicate that differences exist among the mean carat weights for the three certification groups. 
A)  There is sufficient evidence to indicate that differences exist among the mean carat weights for the three certification groups. 
B)  There is sufficient evidence to indicate that the mean carat weight for the HRD group equals the mean carat weight for the IGI group. 
C)  There is sufficient evidence to indicate that the mean carat weight for the GIA group is lower than the other two groups. 
D)  There is insufficient evidence to indicate that differences exist among the mean carat weights for the three certification groups.

Question 4

Four brands of baseball bats were tested to determine which bat allowed hitters to hit a baseball farthest. Eight different batters were thrown 25 pitches while hitting with each of the four bats (assigned in random order). The average distance of the five longest hits using each bat is shown in the table below. The goal is to determine if the average hit distance differs for the four brands of baseball bats.

$\begin{array}{c|c|c|c|c}
\text { Batter } & \text { Brand 1 } & \text { Brand 2 } & \text { Brand 3 } & \text { Brand 4 } \
\hline 1 & 307 & 315 & 300 & 275 \
2 & 310 & 317 & 305 & 285 \
3 & 335 & 335 & 330 & 302 \
4 & 325 & 328 & 320 & 300 \
5 & 300 & 305 & 295 & 270 \
6 & 345 & 350 & 340 & 310 \
7 & 312 & 315 & 308 & 300 \
8 & 298 & 302 & 295 & 288
\end{array}$

The ANOVA table output is shown here:

$\begin{array}{c|c|c|c|c|c}
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\hline \text { Batter } & 7 & 6227.4 & 946.77 & 39.70 & 0.0000 \
\text { Brand } & 3 & 4117.6 & 1372.54 & 57.55 & 0.0000 \
\text { Error } & 21 & 500.9 & 23.85 & & \
\text { Total } & 31 & 11245.9 & & &
\end{array}$

Based on the p-value for this test, make the proper conclusion about the treatments in this experiment.

Accepted Answer

A)  There is insufficient evidence (at $\alpha = 0.01$ ) to indicate differences among the mean distances for the four brands of baseball bats. 
B)  There is sufficient evidence (at $\alpha = 0.01$ ) to indicate differences among the mean distances for the four brands of baseball bats. 
C)  There is sufficient evidence (at $\alpha = 0.01$ ) to indicate differences among the mean distances for the eight batters. 
D)  There is insufficient evidence (at $\alpha = 0.01$ ) to indicate differences among the mean distances for the eight batters. 
A)  There is insufficient evidence (at $\alpha = 0.01$ ) to indicate differences among the mean distances for the four brands of baseball bats. 
B)  There is sufficient evidence (at $\alpha = 0.01$ ) to indicate differences among the mean distances for the four brands of baseball bats. 
C)  There is sufficient evidence (at $\alpha = 0.01$ ) to indicate differences among the mean distances for the eight batters. 
D)  There is insufficient evidence (at $\alpha = 0.01$ ) to indicate differences among the mean distances for the eight batters.

Question 5

A multiple-comparison procedure for comparing four treatment means produced the confidence intervals shown below. Rank the means from smallest to largest. Use solid lines to connect those means which are not significantly different. $$\begin{array} { l } 
\left( \mu _ { 1 } - \mu _ { 2 } \right) : ( 8,20 ) \
\left( \mu _ { 1 } - \mu _ { 3 } \right) : ( - 8,4 ) \
\left( \mu _ { 1 } - \mu _ { 4 } \right) : ( 8,22 ) \
\left( \mu _ { 2 } - \mu _ { 3 } \right) : ( - 22 , - 10 ) \
\left( \mu _ { 2 } - \mu _ { 4 } \right) : ( - 2,4 ) \
\left( \mu _ { 3 } - \mu _ { 4 } \right) : ( 13,21 )
\end{array}$$

Accepted Answer

A)  $24 \overline { 13 }$ 
B)  4213 
C)  $\overline { 41 } \overline { 23 }$ 
D)  $\overline { 42 } \overline { 13 }$ 
A)  $24 \overline { 13 }$ 
B)  4213 
C)  $\overline { 41 } \overline { 23 }$ 
D)  $\overline { 42 } \overline { 13 }$

Question 6

Use the appropriate table to find the following F value: $F _ { 0.05 } , v _ { 1 } = 3 , v _ { 2 } = 28$

Accepted Answer

A)  2.95 
B)  8.62 
C)  3.34 
D)  2.92 
A)  2.95 
B)  8.62 
C)  3.34 
D)  2.92

Question 7

Complete the ANOVA table. 
$$\begin{array} { l c c c c } 
\hline \text { Source } & \text { df } & \text { SS } & \text { MS } & F \
\hline \text { Treatments } & 3 & 857.1 & \
\text { Error } & 8 & 372.8 & \
\hline \text { Total } & & & \
\hline
\end{array}$$

Accepted Answer

None

Question 8

Define the statistical term "treatments."

Accepted Answer

A)  assumptions that are satisfied exactly 
B)  combinations of factor-levels employed in a designed study 
C)  correlations among the factors used in an analysis of variance 
D)  objects on which the responses are measured 
A)  assumptions that are satisfied exactly 
B)  combinations of factor-levels employed in a designed study 
C)  correlations among the factors used in an analysis of variance 
D)  objects on which the responses are measured

Question 9

Four brands of baseball bats were tested to determine which bat allowed hitters to hit a baseball farthest. Eight different batters were thrown 25 pitches while hitting with each of the four bats (assigned in random order). The average distance of the five longest hits using each bat is shown in
The table below. The goal is to determine if the average hit distance differs for the four brands of baseball bats. 
$$\begin{array}{l}
\begin{array} { c | c | c | c | c } 
\text { Batter } & \text { Brand 1 } & \text { Brand 2 } & \text { Brand 3 } & \text { Brand 4 } \
\hline 1 & 307 & 315 & 300 & 275 \
2 & 310 & 317 & 305 & 285 \
3 & 335 & 335 & 330 & 302 \
4 & 325 & 328 & 320 & 300 \
5 & 300 & 305 & 295 & 270 \
6 & 345 & 350 & 340 & 310 \
7 & 312 & 315 & 308 & 300 \
8 & 298 & 302 & 295 & 288
\end{array}\\
\text { A partial ANOVA table is shown below. }\
\begin{array} { l | c | c | c | } 
\text { Source } & \text { DF } & \text { SS } & \text { MS } \
\hline \text { Batter } & 7 & & 946.77 \
\text { Brand } & 3 & & \
\text { Error } & 21 & 500.9 & \
\text { Total } & 31 & 11245.9 &
\end{array}
\end{array}$$ Find the F-value in the table above for testing whether the average distance hit for the four brands of baseball bats differ.

Accepted Answer

A)  39.7 
B)  23.9 
C)  57.6 
D)  2.8 
A)  39.7 
B)  23.9 
C)  57.6 
D)  2.8

Question 10

A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation,
The prices were recorded for each item on the same day at each supermarket. 
$\begin{array} { c l r c c } 
\hline & { \text { Item } } & \text { A } & \text { B } & \text { C } \
\hline \text { 1) } & \text { paper towels } & 1.23 & 1.43 & 1.38 \
\text { 2) } & \text { cereal } & 2.70 & 3.15 & 2.90 \
\text { 3) } & \text { floor cleaner } & 6.09 & 5.97 & 6.98 \
\vert &\vert&\vert&\vert& \vert  \
59 ) & \text { shaving cream } & 1.09 & 0.99 & 1.05 \
60 ) & \text { canned green beans } & 0.55 & 0.70 & 0.47 \
\hline
\end{array}$

Identify the blocks for this experiment.

Accepted Answer

A)  the 60 grocery items 
B)  the $60 \times 3 = 180$ prices 
C)  the three supermarkets 
D)  the day on which the data were collected 
A)  the 60 grocery items 
B)  the $60 \times 3 = 180$ prices 
C)  the three supermarkets 
D)  the day on which the data were collected

Question 11

An appliance manufacturer is interested in determining whether the brand of laundry detergent used affects the average amount of dirt removed from standard household laundry loads. An experiment is set up in which 10 laundry loads are randomly assigned to each of four laundry detergents-Brands A, B, C, and D (a total of 40 loads in the experiment). The amount of dirt removed, y, (measured in milligrams) for each load is recorded and subjected to an ANOVA analysis, including a follow-up Tukey analysis. Which of the following inferences concerning the Tukey results below is incorrect? $\begin{array}{cc}
\text { Brands } & \text { Sample Means } \
\hline \mathrm{D} & 186 \
\mathrm{C} & 177 \
\mathrm{~B} & 142 \
\mathrm{~A} & 131
\end{array}$

Accepted Answer

A)  $\mu _ { \mathrm { C } }  \mu _ { \mathrm { A } }$ 
A)  $\mu _ { \mathrm { C } }  \mu _ { \mathrm { A } }$

Question 12

307 diamonds were sampled and randomly sorted into three groups of diamonds. These diamonds were randomly assigned to one of the three organizations, or groups (HRD, GIA, or IGI), that certify the appraisal of diamonds. A study was conducted to determine if the average size of
Diamonds reported by these three certification groups differ. A completely randomized design was used and the resulting ANOVA table is shown below. $$\begin{array}{l}
\text { One-Way AOV for CARAT by CERT }\
\begin{array} { l c c c l } 
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } \
\hline \text { CERT } & 2 & 8.3265 & 4.16326 & ? ? ? \
\text { Error } & 305 & 15.2604 & 0.05003 & \
\text { Total } & 307 & 23.5869 & &
\end{array}
\end{array}$$ Find the F-value that is missing in the ANOVA table.

Accepted Answer

A)  0.5242 
B)  83.215 
C)  0.5000 
D)  0.0120 
A)  0.5242 
B)  83.215 
C)  0.5000 
D)  0.0120

Question 13

An experiment was conducted to compare the mean iron content in iron ore pieces determined by three different methods: (1) mechanical, (2) manual, and (3) laser. Five 1-meter long pieces of iron ore were removed from a conveyor belt, and the iron content of each piece was determined using each of the three methods. The data are shown below. How should the data be analyzed?

$\begin{array} { l l l l } 
\hline\text { Piece}&\text {  Mechanical}&\text {  Manual }&\text { Laser } \
\hline 1 & 60.34 & 61.37 & 60.31 \
2 & 65.44 & 65.94 & 66.46 \
3 & 60.32 & 60.38 & 61.66 \
4 & 58.34 & 58.37 & 58.21 \
5 & 53.20 & 52.22 & 54.16 \
\hline
\end{array}$

Accepted Answer

A)  randomized block design with three treatments and five blocks 
B)  $3 \times 5$ factorial design 
C)  randomized block design with five treatments and three blocks 
D)  completely randomized design with three treatments 
A)  randomized block design with three treatments and five blocks 
B)  $3 \times 5$ factorial design 
C)  randomized block design with five treatments and three blocks 
D)  completely randomized design with three treatments

Question 14

A certain HMO is attempting to show the benefits of managed health care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that primary specialty is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 28 HMO physicians from each of four primary specialties-- General Practice (GP), Internal Medicine (IM), pediatrics (PED), and Family Physician (FP)-- and recorded the total per-member, per-month charges for each. Identify the treatments for this group.

Accepted Answer

A)  the HMO 
B)  the four specialty groups-GP, IM, PED, and FP 
C)  the total per-member, per-month charges 
D)  the 112 physicians 
A)  the HMO 
B)  the four specialty groups-GP, IM, PED, and FP 
C)  the total per-member, per-month charges 
D)  the 112 physicians

Question 15

Four brands of baseball bats were tested to determine which bat allowed hitters to hit a baseball farthest. Eight different batters were thrown 25 pitches while hitting with each of the four bats (assigned in random order). The average distance of the five longest hits using each bat is shown in the table below. The goal is to determine if the average hit distance differs for the four brands of baseball bats.

$$\begin{array} { c | c | c | c | c } 
\text { Batter } & \text { Brand 1 } & \text { Brand 2 } & \text { Brand 3 } & \text { Brand 4 } \
\hline 1 & 307 & 315 & 300 & 275 \
2 & 310 & 317 & 305 & 285 \
3 & 335 & 335 & 330 & 302 \
4 & 325 & 328 & 320 & 300 \
5 & 300 & 305 & 295 & 270 \
6 & 345 & 350 & 340 & 310 \
7 & 312 & 315 & 308 & 300 \
8 & 298 & 302 & 295 & 288
\end{array}$$ How should the data be analyzed?

Accepted Answer

A)  Completely randomized design with four treatments 
B)  4 × 8 factorial design 
C)  Randomized block design with four treatments and eight blocks 
D)  Randomized block design with eight treatments and four blocks 
A)  Completely randomized design with four treatments 
B)  4 × 8 factorial design 
C)  Randomized block design with four treatments and eight blocks 
D)  Randomized block design with eight treatments and four blocks

Question 16

A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket.
The results of the ANOVA are summarized in the following table. $$\begin{array} { l r r r r r } 
\text { Source } & \text { df } & \text { Anova SS } & \text { Mean Square } & \text { F Value } & \text { Pr > F } \
\hline \text { Supermkt } & 2 & 2.6412678 & 1.3206399 & 39.23 & 0.0001 \
\text { Item } & 59 & 215.5949311 & 3.6541514 & 108.54 & 0.0001 \
\text { Error } & 118 & 3.9725322 & 0.0336655 & &
\end{array}$$ Based on the p-value of the test, make the proper conclusion.

Accepted Answer

A)  There is sufficient evidence (at $\alpha = .01$ ) to indicate that the mean prices of grocery items at the three supermarkets are identical. 
B)  There is insufficient evidence (at $\alpha = .01$ ) to indicate differences among the mean prices of grocery items at the three supermarkets. 
C)  There is sufficient evidence (at $\alpha = .01$ ) to indicate differences among the mean prices of grocery items at the three supermarkets. 
D)  No conclusions can be drawn from the given information. 
A)  There is sufficient evidence (at $\alpha = .01$ ) to indicate that the mean prices of grocery items at the three supermarkets are identical. 
B)  There is insufficient evidence (at $\alpha = .01$ ) to indicate differences among the mean prices of grocery items at the three supermarkets. 
C)  There is sufficient evidence (at $\alpha = .01$ ) to indicate differences among the mean prices of grocery items at the three supermarkets. 
D)  No conclusions can be drawn from the given information.

Question 17

Find the critical value F0 for a one-tailed test using $\alpha = 0.05$ with 8 numerator degrees of freedom and 15 denominator degrees of freedom

Accepted Answer

A)  3.20 
B)  3.22 
C)  4.10 
D)  2.64 
A)  3.20 
B)  3.22 
C)  4.10 
D)  2.64

Question 18

Find the following: $P ( F \leq 2.71 ) \text {, for } v _ { 1 } = 5 , v _ { 2 } = 20$

Accepted Answer

A)  0.05 
B)  0.025 
C)  0.975 
D)  0.95 
A)  0.05 
B)  0.025 
C)  0.975 
D)  0.95

Question 19

The variable measured in the study is called __________.

Accepted Answer

A)  the response variable 
B)  the treatment 
C)  a sampling unit 
D)  the factor level 
A)  the response variable 
B)  the treatment 
C)  a sampling unit 
D)  the factor level

Question 20

Complete the ANOVA table. 
$\begin{array}{lccc}
\text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } \
\hline \text { A } & 3 & & 170.90 \ 
\text { B } & 1 & 411.80 \
\text { AB } & & & 305.10 \
\text { ERROR } & & & \
\hline \text { Total } & 23 & 5643.00 &
\end{array}$

Accepted Answer

\[\begin{array} { l c c c c } 
\text { S

__________ is a particular combination of levels of the factors involved in a study.

A multiple-comparison procedure for comparing four treatment means produced the confidence intervals shown below. Rank the means from smallest to largest. Use solid lines to connect those means which are not significantly different. - :(8,20) - :(-8,4) - :(8,22) - :(-22,-10) - :(-2,4) - :(13,21)

Use the appropriate table to find the following F value: $F _ { 0.05 } , v _ { 1 } = 3 , v _ { 2 } = 28$

Complete the ANOVA table. Source df SS MS F Treatments 3 857.1 Error 8 372.8 Total

Define the statistical term "treatments."

Find the critical value F0 for a one-tailed test using $\alpha = 0.05$ with 8 numerator degrees of freedom and 15 denominator degrees of freedom

Find the following: $P ( F \leq 2.71 ) \text {, for } v _ { 1 } = 5 , v _ { 2 } = 20$

The variable measured in the study is called __________.

Complete the ANOVA table. Source df SS MS F A 3 170.90 B 1 411.80 AB 305.10 ERROR Total 23 5643.00

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Random Variables and Probability Distributions

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single Sample: 355 Tests of Hypotheses

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Categorical Data Analysis

Simple Linear Regression

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Nonparametric Statistics Available on CD

Filters

Exam 9: Design of Experiments and Analysis of Variance

__________ is a particular combination of levels of the factors involved in a study.

A multiple-comparison procedure for comparing four treatment means produced the confidence intervals shown below. Rank the means from smallest to largest. Use solid lines to connect those means which are not significantly different. - :(8,20) - :(-8,4) - :(8,22) - :(-22,-10) - :(-2,4) - :(13,21)

Use the appropriate table to find the following F value: F0.05,v1=3,v2=28F _ { 0.05 } , v _ { 1 } = 3 , v _ { 2 } = 28F0.05​,v1​=3,v2​=28

Complete the ANOVA table. Source df SS MS F Treatments 3 857.1 Error 8 372.8 Total

Define the statistical term "treatments."

Find the critical value F0 for a one-tailed test using α=0.05\alpha = 0.05α=0.05 with 8 numerator degrees of freedom and 15 denominator degrees of freedom

Find the following: P(F≤2.71), for v1=5,v2=20P ( F \leq 2.71 ) \text {, for } v _ { 1 } = 5 , v _ { 2 } = 20P(F≤2.71), for v1​=5,v2​=20

The variable measured in the study is called __________.

Complete the ANOVA table. Source df SS MS F A 3 170.90 B 1 411.80 AB 305.10 ERROR Total 23 5643.00

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Random Variables and Probability Distributions

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single Sample: 355 Tests of Hypotheses

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Categorical Data Analysis

Simple Linear Regression

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Nonparametric Statistics Available on CD

Filters

Use the appropriate table to find the following F value: $F _ { 0.05 } , v _ { 1 } = 3 , v _ { 2 } = 28$

Find the critical value F0 for a one-tailed test using $\alpha = 0.05$ with 8 numerator degrees of freedom and 15 denominator degrees of freedom

Find the following: $P ( F \leq 2.71 ) \text {, for } v _ { 1 } = 5 , v _ { 2 } = 20$