Deck 10: Analysis of Variance: Comparing More Than Two Means

Question 1

An advertising firm conducts 3 different campaigns, each in 14 different cities, to promote a certain product, and tracks the product sales attributable to each campaign in each city. Determine
Whether the study is observational or designed.

A)observational
B)designed

Answer 1

B

Question 2

Use the appropriate table to find the following F value:

Answer 2

C

Question 3

A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that
Certification level is an important factor in measuring the cost-effectiveness of physicians. To
Investigate this, the HMO obtained independent random samples of 27 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 per month charges for each (a total of 81
Physicians). How many factors are present in this study?

A)81
B)3
C)1
D)27

Answer 3

C

Question 4

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 25 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.

A)the total per-member, per-month charges
B)the HMO
C)the 100 physicians
D)the four specialty groupsGP, IM, PED, and FP

Question 5

The intensity of a factor is called __________.

A)the design
B)the treatment
C)a factor level
D)the experimental unit

Question 6

The variables, quantitative or qualitative, whose effect on a response variable is of interest are called __________.

A)the treatments
B)the experimental units
C)factors
D)the factor level

Question 7

Define the statistical term ʺtreatments.ʺ

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

Question 8

A counselor obtains SAT averages for incoming freshmen each year for a period covering 14 years, with the objective of determining the relationship between the SAT score and the year the test was
Given. The averages are then subjected to analysis for the purpose of drawing a conclusion
Regarding a trend. Determine whether the study is observational or designed.

A)designed
B)observational

Question 9

In a study to determine the least amount of time necessary to clean an SUV while maintaining a high quality standard, the owner of a chain of car washes designed an experiment where 20
Employees were divided into four groups, each with five members. Each member of each group
Was assigned an SUV to clean within a certain time limit. The time limits for the groups were 20
Minutes, 25 minutes, 30 minutes, and 35 minutes. After the time limits for each group had expired,
The owner inspected each SUV and rated the quality of the cleaning job on a scale of 1 to 10. What
Are the possible values of the response variable?

A)the time limits: 20 min, 25 min, 30 min, 35 min
B)the number of employees in each group: 5
C)the number of groups: 4
D)the quality ratings: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Question 10

Find the following:

Question 11

The variable measured in the study is called __________.

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

Question 12

In a study to determine the least amount of time necessary to clean an SUV while maintaining a high quality standard, the owner of a chain of car washes designed an experiment where 20
Employees were divided into four groups, each with five members. Each member of each group
Was assigned an SUV to clean within a certain time limit. The time limits for the groups were 20
Minutes, 25 minutes, 30 minutes, and 35 minutes. After the time limits for each group had expired,
The owner inspected each SUV and rated the quality of the cleaning job on a scale of 1 to 10. What
Are the factor levels for this study?

A)the quality ratings: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
B)the number of employees in each group: 5
C)the number of groups: 4
D)the time limits: 20 min, 25 min, 30 min, 35 min

Question 13

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

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

Question 14

A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that
Certification level is an important factor in measuring the cost-effectiveness of physicians. To
Investigate this, the HMO obtained independent random samples of 22 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, per-month charges for each (a total of 66
Physicians). Identify the dependent (response)variable for this study.

A)the total per-member, per-month charge
B)the three certifications groups C, E, and I
C)the HMO
D)the 66 physicians

Question 15

An industrial psychologist is investigating the effects of work environment on employee attitudes. A group of 44 recently hired sales trainees were randomly assigned to one of 11 different ʺhome
Roomsʺ - four trainees per room. Each room is identical except for wall color, with 11 different
Colors used. The psychologist wants to know whether room color has an effect on attitude, and, if
So, wants to compare the mean attitudes of the trainees assigned to the 11 room colors. At the end
Of the training program, the attitude of each trainee was measured on a 100-pt. scale (the lower the
Score, the poorer the attitude). How many treatments are in this study?

A)100
B)4
C)44
D)11

Question 16

A scientist is hoping to compare the mean levels of DDT toxin found in three species of fish in a local river. He randomly samples 50 of each species to use in the analysis. For each fish, he
Measures the amount of DDT toxin present. Ideally he will be able to rank the species based on the
Mean level of toxin found in each of the three species. Identify the treatments for this study.

A)The three fish species
B)The amount of DDT in a fish
C)The 50 fish
D)The scientist

Question 17

A scientist is hoping to compare the mean levels of DDT toxin found in three species of fish in a local river. He randomly samples 50 of each species to use in the analysis. For each fish, he
Measures the amount of DDT toxin present. Ideally he will be able to rank the species based on the
Mean level of toxin found in each of the three species. Identify the response variable in this study.

A)The scientist
B)The amount of DDT in a fish
C)The three fish species
D)The number of fish

Question 18

A city monitors ozone levels weekly over a 4 year period in order to relate the ozone levels to the seasons. Determine whether the study is observational or designed.

A)designed
B)observational

Question 19

Find the following:

Question 20

A scientist is hoping to compare the mean levels of DDT toxin found in three species of fish in a local river. He randomly samples 50 of each species to use in the analysis. For each fish, he
Measures the amount of DDT toxin present. Ideally he will be able to rank the species based on the
Mean level of toxin found in each of the three species. How many factors are present in this study?

A)3
B)50
C)6
D)1

Question 21

Question 22

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.

Question 23

Four different leadership styles used by Big-Six accountants were investigated. As part of a designed study, 15 accountants were randomly selected from each of the four leadership style
Groups (a total of 60 accountants). Each accountant was asked to rate the degree to which their
Subordinates performed substandard field work on a 10-point scalecalled the ʺsubstandard work
Scaleʺ. The objective is to compare the mean substandard work scales of the four leadership styles.
The data on substandard work scales for all 60 observations were subjected to an analysis of
Variance.

Question 24

A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that
Certification level is an important factor in measuring the cost-effectiveness of physicians. To
Investigate this, the HMO obtained independent random samples of 25 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, per-month charges for each (a total of 25
Physicians). In order to compare the mean charges for the three groups, the data will be subjected
To an analysis of variance. Write the null hypothesis tested by the ANOVA.

Question 25

A multiple-comparison procedure for comparing four treatment means produced the confidence intervals shown below. For each pair of means, indicate which mean is larger or indicate that there
Is no significant difference.

Question 26

Complete the ANOVA table.

Question 27

A partially completed ANOVA table for a completely randomized design is shown here.

Question 28

A company that employs a large number of salespeople is interested in learning which of
the salespeople sell the most: those strictly on commission, those with a fixed salary, or
those with a reduced fixed salary plus a commission. The previous monthʹs records for a
sample of salespeople are inspected and the amount of sales (in dollars)is recorded for
each, as shown in the table.

Question 29

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.

Question 30

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.

Question 31

A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that
Certification level is an important factor in measuring the cost-effectiveness of physicians. To
Investigate this, the HMO obtained independent random samples of 29 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, per-month charges for each (a total of 87
Physicians). In order to compare the mean charges for the three groups, the data will be subjected
To an analysis of variance. Give the degrees of freedom appropriate for conducting the ANOVA
F-test.

Question 32

Question 33

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

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

Question 34

An industrial psychologist is investigating the effects of work environment on employee attitudes. A group of 20 recently hired sales trainees were randomly assigned to one of four different ʺhome
Roomsʺ five trainees per room. Each room is identical except for wall color. The four colors used
Were light green, light blue, gray, and red. The psychologist wants to know whether room color
Has an effect on attitude, and, if so, wants to compare the mean attitudes of the trainees assigned to
The four room colors. At the end of the training program, the attitude of each trainee was measured
On a 60-pt. scale (the lower the score, the poorer the attitude). The data was subjected to a
One-way analysis of variance.

Question 35

Given that the mean square for treatments (MST)for an ANOVA F-test is 5,000 and the mean square for error (MSE)is 3,750, find the value of the test statistic F.

A)1.25
B).800
C)1.33
D).750

Question 36

Which of the following is not a condition required for a valid ANOVA F-test for a completely randomized experiment?

A)The sample chosen from each of the populations is sufficiently large.
B)The sampled populations all have distributions that are approximately normal.
C)The variances of all the sampled populations are equal.
D)The samples are chosen from each population in an independent manner.

Question 37

In a completely randomized design experiment, 10 experimental units were randomly
chosen for each of three treatment groups and a quantity was measured for each unit
within each group. In the first steps of testing whether the means of the three groups are
the same, the sum of squares for treatments was calculated to be 3,110 and the sum of
squares for error was calculated to be 27,000.
Complete the ANOVA table.

Question 38

Given that the sum of squares for treatments (SST)for an ANOVA F-test is 9,000 and there are four total treatments, find the mean square for treatments (MST).

A)2,250
B)1,500
C)3,000
D)1,800

Question 39

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.

Question 40

Given that the sum of squares for error (SSE)for an ANOVA F-test is 12,000 and there are 40 total experimental units with eight total treatments, find the mean square for error (MSE).

A)400
B)375
C)308
D)300

Question 41

Which of the following is not one of the multiple comparison method options available to compare treatment means?

A)The Bonferroni Method
B)The Scheffe Method
C)The Einstein Method
D)The Tukey Method

Question 42

Consider a completely randomized design with k treatments. Assume all pairwise comparisons of treatment means are to be made using a multiple comparisons procedure. Determine the total
Number of treatment means to be compared for the value k = 4.

A)4
B)6
C)10
D)8

Question 43

In an experiment with 10 treatments, how many pairs of means can be compared?

A)90
B)20
C)100
D)45

Question 44

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 Bonferroni multiple comparison results are shown below.

Question 45

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 20 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. In order to compare the mean charges for the four specialty groups, the data were
Be subjected to a one-way analysis of variance. The results of the Tukey analysis are summarized
Below.

Question 46

Which method generally produces wider confidence intervals?

A)Scheffé
B)Tukey
C)ANOVA
D)Bonferroni

Question 47

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. Identify the treatments for this experiment.

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

Question 48

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. Identify the response variable in this experiment.

A)A batter
B)The brand of bat
C)The brand of baseball
D)The average distance hit

Question 49

Consider a completely randomized design with five treatments. How many pairwise comparisons of treatments are made in a Bonferroni analysis?

A)5! = 120
B)10
C)5
D)20

Question 50

The results of a Tukey multiple comparison are summarized below.

Question 51

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?

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

Question 52

An economist is investigating the impact of todayʹs economy on workers in the manufacturing industry who have been laid off. A sample of 50 workers was randomly selected from all workers
In manufacturing that have been laid off in the past year. The following variables were measured
For each laid off worker: length of time jobless (number of weeks)and tax status (single, married,
Or married/head of household). The data for the 50 workers were entered into the computer and
Analyzed to determine if the mean number of weeks jobless differed for the three tax status groups.
The Tukey multiple comparison printout is shown below:

Question 53

Which procedure was specifically developed for pairwise comparisons when the sample sizes of the treatments are equal?

A)Tukey
B)ANOVA
C)Scheffé
D)Bonferroni

Question 54

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. How should the data be analyzed?

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

Question 55

Question 56

A multiple-comparison procedure for comparing four treatment means produced the confidence intervals shown below. For each pair of means, indicate which mean is larger or indicate that there
Is no significant difference.

Question 57

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?

Question 58

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. Identify the dependent (response)variable for this experiment.

A)the supermarkets
B)the prices of the grocery items
C)the mean prices of the grocery items at each supermarket
D)the grocery items

Question 59

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.

Question 60

The __________ in a designed experiment to compare k means is the probability of making
at least one Type I error in a series of inferences about the population means, based on (1 -
α)100% confidence intervals.

Question 61

Question 62

When a variable is identified as reducing variation in the response variable, but no additional
knowledge concerning the variable is desired, it should be used as the blocking factor in the
randomized block design.

Question 63

The randomized block design is an extension of the matched pairs comparison of μ1 and μ2.

Question 64

A study was conducted to test the effectiveness of supermarket sales strategies. At one supermarket, the price level (regular, reduced price, and at cost to supermarket)and display level
(normal display space, normal display space plus end-of-aisle display, and twice the normal
Display space)were tested to determine if they had any effect on the weekly sales of a particular
Supermarket product. Each of the combinations of price level and display level were put in place
For a randomly selected week and the weekly sales of the product was recorded. Each combination
Was used three times over the course of the experiment. The results of the study are shown here:

Question 65

Psychologists have found that people are generally reluctant to transmit bad news to their peers. This phenomenon has been named the ʺMUM effect.ʺ To investigate the cause of the MUM effect,
Undergraduates at a university participated in an experiment. Each subject was asked to
Administer an IQ test to another student and then provide the test taker with his or her percentile
Score. (Unknown to the subject, the test taker was a bogus student who was working with the
Researchers.)The experimenters manipulated two factors, subject visibility and success of test
Taker, each at two levels. Subject visibility was either visible or not visible to the test taker. Success
Of test taker was either top 20% or bottom 20%. Ten subjects were randomly assigned to each of the
2 x 2 = 4 experimental conditions. Then the time (in seconds)between the end of the test and the
Delivery of the percentile score from the subject to the test taker was measured. (This variable is
Called the latency to feedback.)What type of experimental design was employed in this study?

A)completely randomized design with four treatments
B)randomized block design with four treatments and 10 blocks
C)2 x 2 factorial design with 10 replications
D)4 x 20 factorial design with no replications

Question 66

A market research firm is interested in the possible success of new flavors of ice cream. A
study was conducted with three different flavorspeach, almond, and coconut. Three
participants were given a sample of each ice cream, in random order, and asked to rate the
flavors on a 100-point scale. The results are given in the table below.

Question 67

An experiment was conducted using a randomized block design. The data from the
experiment are displayed in the following table.

Question 68

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. Fully interpret the Bonferroni analysis.

Question 69

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. Identify the blocks for this experiment.

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

Question 70

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. A partial ANOVA table is shown below. Find the F-value in the table above for testing whether the average distance hit for the four brands
Of baseball bats differ.

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

Question 71

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.

Question 72

The goal of an experiment is to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, we want to determine whether the effect of directional
Aid (wall signs or map)on travel time depends on starting room location (interior or exterior).
Three visitors were assigned to each of the combinations of directional aid and starting room
Location, and the travel times of each (in seconds)to reach the goal destination room were
Recorded.

Question 73

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 12 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.)A manufacturer of
Brand A claims that the design of the experiment is flawed. According to the manufacturer, Brand
A is better in cold water than in hot water. If all 48 loads in the above experiment were run in hot
Water, the results will be biased against Brand A. Explain how to redesign the experiment so that
The main effects of both brand and water temperature (hot or cold)on amount of dirt removed,
And their possible interaction, can be investigated.

Question 74

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. Identify the test statistic that should be used for testing whether the average distance hit for the
Four brands of baseball bats differ.

A)39.7
B)57.55
C)0.0000
D)23.85

Question 75

Suppose a company makes 4 different frozen dinners, and tests their ability to attract customers. They test the frozen dinners in 13 different stores in order to account for any extraneous sources of
Variation. The company records the number of customers who purchase each product at each
Store. What assumptions are necessary for the validity of the F statistic for comparing the response
Means of the 4 frozen dinners?

A)The means of the observations corresponding to all the block-treatment combinations are equal, and the variances of all the probability distributions are equal.
B)The probability distributions of observations corresponding to all the block-treatment combinations are normal, and the sampling distributions of the variances of all the
Block-treatment combinations are normally distributed.
C)The probability distributions of observations corresponding to all the block-treatment combinations are normal, and the variances of all the probability distributions are equal.
D)None. The Central Limit Theorem eliminates the need for any assumptions.

Question 76

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.

Question 77

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 both primary specialty and whether the physician is a foreign or USA medical school
Graduate are an important factors in measuring the cost-effectiveness of physicians. To investigate
This, the president obtained independent random samples of 40 HMO physicians, half foreign
Graduates and half USA graduates, 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. Thus, information on charges were obtained for a total
Of n = 160 doctors. The sample mean charges for each of the eight categories are shown in the
Table.

Question 78

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.

Question 79

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.

Question 80

A study was conducted to test the effectiveness of supermarket sales strategies. At one supermarket, the price level (regular, reduced price, and at cost to supermarket)and display level
(normal display space, normal display space plus end-of-aisle display, and twice the normal
Display space)were tested to determine if they had any effect on the weekly sales of a particular
Supermarket product. Each of the combinations of price level and display level were put in place
For a randomly selected week and the weekly sales of the product was recorded. Each combination
Was used three times over the course of the experiment. The results of the study are shown here: