Find the test statistic F to test the hypothesis that the populations have the same mean. Use α = 0.05. \[\begin{array} { l l l } \hline \text { Brand 1 } & \text { Brand 2 } & \text { Brand 3 } \\ \hline \mathrm { n } _ { 1 } = 8 & \mathrm { n } _ { 2 } = 8 & \mathrm { n } _ { 3 } = 8 \\ \overline { \mathrm { x } } 1 = 3.0 & \overline { \mathrm { x } } 2 = 2.6 & \overline { \mathrm { x } } 3 = 2.6 \\ \mathrm {~s} _ { 1 } = 0.50 & \mathrm {~s} _ { 2 } = 0.60 & \mathrm {~s} 3 = 0.55 \end{array}\]

A) 1.403 B) 1.021 C) 1.182 D) 0.832 A) 1.403 B) 1.021 C) 1.182 D) 0.832 A

The times (in minutes) to assemble a component for three different cell phones are listed below. Use α= 0.01.Which of the following is correct? \[\begin{array} { c | c | c } \text { Phone } 1 & \text { Phone } 2 & \text { Phone } 3 \\ \hline 32 & 40 & 25 \\ 30 & 29 & 31 \\ 31 & 38 & 29 \\ 32 & 33 & 28 \\ 33 & 36 & \\ 31 & 32 & \\ & 35 & \end{array}\]

A) The mean time to assemble Phone 1 is the same as the mean time to assemble Phone 2. B) The mean time to assemble Phone 1 is different from the mean time to assemble Phone 3. C) The mean time to assemble Phone 2 is the same as the mean time to assemble Phone 3. D) There is not enough evidence to suggest that the means are different. A) The mean time to assemble Phone 1 is the same as the mean time to assemble Phone 2. B) The mean time to assemble Phone 1 is different from the mean time to assemble Phone 3. C) The mean time to assemble Phone 2 is the same as the mean time to assemble Phone 3. D) There is not enough evidence to suggest that the means are different.

A researcher wishes to test $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 }$ against $\mathrm { H } _ { 1 }$ :at least one of the means is different. Based on the ANOVA table below, what is the mean square due to error? $\begin{array} { l c c c c c } \text { SOURCE } & \text { df } & \text { SS } & \text { MS } & \text { F } & p \\ \hline \text { Treatments } & 2 & 86.22 & 43.11 & 13.15 & 0.0174 \\ \text { Blocks } & 2 & 0.889 & 0.444 & 0.136 & 0.8767 \\ \text { Error } & 4 & 13.11 & 3.28 & & \\ \\ \hline \text { Total } & 8 & 100.22 & & & \end{array}$

A) 3.28 B) 13.11 C) 0.444 D) 0.136 A) 3.28 B) 13.11 C) 0.444 D) 0.136

Find the critical F0-value to test the hypothesis that the populations have the same mean. Use α= 0.05. \[\begin{array} { l c c } \hline \text { Brand 1 } & \text { Brand 2 } & \text { Brand 3 } \\ \hline \mathrm { n } _ { 1 } = 8 & \mathrm { n } _ { 2 } = 8 & \mathrm { n } _ { 3 } = 8 \\ \overline { \mathrm { x } } 1 = 3.0 & \overline { \mathrm { x } } 2 = 2.6 & \overline { \mathrm { x } } 3 = 2.6 \\ \mathrm {~s} _ { 1 } = 0.50 & \mathrm {~s} _ { 2 } = 0.60 & \mathrm {~s} _ { 3 } = 0.55 \\ \hline \end{array}\]

A) 3.49 B) 3.210 C) 2.819 D) 1.892 A) 3.49 B) 3.210 C) 2.819 D) 1.892

A realtor wishes to compare the square footage of houses in 4 different towns, all of which are pricedapproximately the same. The data are listed below. Can the realtor conclude that the mean square footage inthe four towns are equal? Use α = 0.01. \[\begin{array} { c c c c } \hline \text { Town 1 } & \text { Town 2 } & \text { Town } 3 & \text { Town 4 } \\ \hline 2150 & 1780 & 1530 & 2400 \\ 2000 & 1540 & 1670 & 2350 \\ 1980 & 1690 & 1580 & 2600 \\ 2210 & 1650 & 1600 & 2150 \\ 1900 & & 1500 & 2000 \\ & & 1750 & 2200 \\ & & & 2350 \\ \hline \end{array}\]

critical value @#LAT-DLM&; test statisti

Exam 13: Comparing Three or More Means

Find the test statistic F to test the hypothesis that the populations have the same mean. Use α = 0.05. Brand 1 Brand 2 Brand 3 =8 =8 =8 1=3.0 2=2.6 3=2.6 =0.50 =0.60 3=0.55

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Question 1

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A

Four different types of insecticides are used on strawberry plants. The number of strawberries on eachrandomly selected plant is given below. Test the hypothesis that the type of insecticide makes no difference inthe mean number of strawberries per plant. Use α = 0.01. Insecticide 1 Insecticide 2 Insecticide 3 Insecticide 4 6 5 6 3 7 8 3 5 6 5 3 3 5 5 4 4 7 5 2 4 6 6 3 5

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critical value $\mathrm { F } _ { 0.01,3,20 } = 4.94$ ; test statistic $\mathrm { F } \approx 8.357$ ; reject $\mathrm { H } _ { 0 }$ ; The data provides ample evidence that the sample means are unequal.

A researcher wishes to determine whether there is a difference in the average age of middle school, highschool, and college teachers. Teachers are randomly selected. Their ages are recorded below. Use α = 0.01.Which of the following is a correct statement about the means? Middle School Teachers High School Teachers College Teachers 23 41 36 28 36 45 27 38 39 37 47 61 25 42 45 52 31 35

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A

Four different types of insecticides are used on strawberry plants. The number of strawberries on eachrandomly selected plant is given below. Use α = 0.01. Which of the following is a correct statement about themeans? Insecticide 1 Insecticide 2 Insecticide 3 Insecticide 4 6 5 6 3 6 8 3 5 5 5 3 3 7 5 2 4 7 5 4 4 6 6 3 5

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Question 4

A medical researcher wishes to try three different techniques to lower cholesterol levels of patients with highcholesterol levels. The subjects are randomly selected and assigned to one of three groups. Group 1 is givenmedication, Group 2 is given an exercise program, and Group 3 is assigned a diet program. At the end of sixweeks, each subject?s cholesterol level is recorded. Find the test statistic F to test the hypothesis that there is nodifference among the means. Use ? = 0.05. Group 1 Group 2 Group 3 13 8 4 12 2 12 9 3 4 15 5 6 11 4 9 8 0 8

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Question 5

The times (in minutes) to assemble a component for three different cell phones are listed below. Use α= 0.01.Which of the following is correct? Phone 1 Phone 2 Phone 3 32 40 25 30 29 31 31 38 29 32 33 28 33 36 31 32 35

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Question 6

How, in general, is the requirement of equal population variances to allow the use of analysis of variancemethod verified?

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Question 7

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Question 8

A researcher wishes to determine whether there is a difference in the average age of middle school, highschool, and college teachers. Teachers are randomly selected. Their ages are recorded. State the requirementsthat must be satisfied in order to use the one-way ANOVA procedure.

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Question 9

True or False: It is required for the Two-Way ANOVA that the populations from which the samples are drawnare normal.

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Question 10

A researcher wishes to test $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 }$ against $\mathrm { H } _ { 1 }$ :at least one of the means is different. Based on the ANOVA table below, what is the mean square due to error? SOURCE df SS MS F p Treatments 2 86.22 43.11 13.15 0.0174 Blocks 2 0.889 0.444 0.136 0.8767 Error 4 13.11 3.28 Total 8 100.22

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Question 11

The grade point averages of students participating in sports at a local college are to be compared. The data arelisted below. Test the hypothesis that there is no difference in the mean grade point averages of the 3 groups.Use α = 0.05. Hockey Track Basketball 2.6 1.8 2.7 3.2 1.9 2.5 2.5 2.1 2.8 3.5 3.3 3.0 3.1 2.5 2.1

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Question 12

A medical researcher wishes to try three different techniques to lower cholesterol levels of patients with highcholesterol levels. The subjects are randomly selected and assigned to one of three groups. Group 1 is givenmedication, Group 2 is given an exercise program, and Group 3 is assigned a diet program. At the end of sixweeks, each subject?s cholesterol level is recorded. Find the critical value F-value to test the hypothesis thatthere is no difference among the means. Use ? = 0.05. Group 1 Group 2 Group 3 9 8 6 12 2 12 11 3 4 15 5 4 13 4 9 8 0 8

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Question 13

A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMObelieves that certain types of doctors are more cost-effective than others. One theory is that Certification Levelis an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtainedindependent random samples of 20 physicians from each of the three certification levels-- Board certified (C);Uncertified, board eligible (E); and Uncertified, board ineligible (I)-- and recorded the total per member permonth charges for each (a total of 60 physicians). In order to compare the mean charges for the three groups,the data will be subjected to an analysis of variance. The results of the ANOVA are summarized in thefollowing table. Take α = 0.01. Interpret the P-value of the ANOVA F test. Source df SS MS F Value \multicolumn 2 c Prob > F Treatments 2 3752.13 1876.065 20.73 0.0001 Error 57 5158.5 90.5 Total 59 8910.63

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Question 14

Find the critical F0-value to test the hypothesis that the populations have the same mean. Use α= 0.05. Brand 1 Brand 2 Brand 3 =8 =8 =8 1=3.0 2=2.6 3=2.6 =0.50 =0.60 =0.55

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Question 15

A builder has two crews that construct homes. He is interested in determining if there is a difference in thetime it takes the crews to build three different styles of homes. The time in days for each crew is given below.What type of interaction is revealed by the interaction plot? Test at α = 0.05. Cottage Bi-Level 2 story Smith 27,34,30,35,39 25,47,44,30,39 28,24,29,32,41 Jones 46,41,37,26,24 31,39,44,45,32 43,45,44,36,31

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Question 16

A training program is supposed to develop self confidence in managers. The two-week program isadministered to six males and six females. All participants are tested after the end of the first week and afterthe end of the second week. The scores of those tests are given below. What type of interaction is revealed bythe interaction plot? Test at α = 0.05. Week One Week Two Men 65,81,81,75,88,75 90,94,80,91,81,98 Women 71,76,82,88,87,75 81,97,86,91,99,83

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Question 17

Why is the completely randomized block design not always sufficient?13.4 Two-Way Analysis of Variance1 Analyze a two-way ANOVA design, and perform the Tukey test as needed.

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Question 18

A realtor wishes to compare the square footage of houses in 4 different towns, all of which are pricedapproximately the same. The data are listed below. Can the realtor conclude that the mean square footage inthe four towns are equal? Use α = 0.01. Town 1 Town 2 Town 3 Town 4 2150 1780 1530 2400 2000 1540 1670 2350 1980 1690 1580 2600 2210 1650 1600 2150 1900 1500 2000 1750 2200 2350

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Question 19

The times (in minutes) to assemble a component for 3 different cell phones are listed below. Workers arerandomly selected. Test the hypothesis that there is no difference in the mean time for each cell phone. Use α =0.01. Phone 1 Phone 2 Phone 3 32 40 28 32 29 25 31 38 29 30 33 31 33 32 31 36 35

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Question 20

Find the test statistic F to test the hypothesis that the populations have the same mean. Use α = 0.05. Brand 1 Brand 2 Brand 3 =8 =8 =8 1=3.0 2=2.6 3=2.6 =0.50 =0.60 3=0.55

The times (in minutes) to assemble a component for three different cell phones are listed below. Use α= 0.01.Which of the following is correct? Phone 1 Phone 2 Phone 3 32 40 25 30 29 31 31 38 29 32 33 28 33 36 31 32 35

How, in general, is the requirement of equal population variances to allow the use of analysis of variancemethod verified?

A researcher wishes to determine whether there is a difference in the average age of middle school, highschool, and college teachers. Teachers are randomly selected. Their ages are recorded. State the requirementsthat must be satisfied in order to use the one-way ANOVA procedure.

True or False: It is required for the Two-Way ANOVA that the populations from which the samples are drawnare normal.

Find the critical F0-value to test the hypothesis that the populations have the same mean. Use α= 0.05. Brand 1 Brand 2 Brand 3 =8 =8 =8 1=3.0 2=2.6 3=2.6 =0.50 =0.60 =0.55

Why is the completely randomized block design not always sufficient?13.4 Two-Way Analysis of Variance1 Analyze a two-way ANOVA design, and perform the Tukey test as needed.

The times (in minutes) to assemble a component for 3 different cell phones are listed below. Workers arerandomly selected. Test the hypothesis that there is no difference in the mean time for each cell phone. Use α =0.01. Phone 1 Phone 2 Phone 3 32 40 28 32 29 25 31 38 29 30 33 31 33 32 31 36 35

Data Collection

Organizing and Summarizing Data

Numerically Summarizing Data

Describing the Relation Between Two Variables

Probability

Discrete Probability Distributions

The Normal Probability Distribution

Sampling Distributions

Estimating the Value of a Parameter

Hypothesis Tests Regarding a Parameter

Inferences on Two Samples

Inference on Categorical Data

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