Exam 13: Comparing Three or More Means

Four different types of insecticides are used on strawberry plants. The number of strawberries on eachrandomly selected plant is recorded. State the requirements that must be satisfied in order to use the one-wayANOVA procedure.

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 subjectʹs cholesterol level is recorded. Test the hypothesis that there is no difference among themeans. Use α = 0.05. Group 1 Group 2 Group 3 9 8 6 12 5 12 11 2 4 15 3 8 13 4 9 8 0 4

Four different types of insecticides are used on strawberry plants. The number of strawberries on eachrandomly selected plant is given below. Find the test statistic F to test the hypothesis that the type of insecticidemakes no difference in the mean number of strawberries per plant. Use α = 0.01. Insecticide 1 Insecticide 2 Insecticide 3 Insecticide 4 6 5 6 3 5 8 3 5 6 5 4 3 7 5 3 4 7 5 2 5 6 6 3 4

Find the critical value from the Studentized range distribution for H0: μ1 = μ2 = μ3 = μ4 = μ5, with n = 18 atα = 0.01.

The grade point averages of students participating in sports at a local community college are to be compared.The data are listed below. Which of the following is a correct statement about the means? Use α = 0.05. Hockey Track Basketball 2.6 1.8 2.5 3.2 2.1 2.7 2.5 1.9 2.8 3.5 3.3 3.0 3.1 2.5 2.1

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. Use α = 0.01. Which of the following is correct? Town 1 Town 2 Town 3 Town 4 2150 1780 1530 2400 1980 1540 1670 2350 2210 1690 1580 2600 2000 1650 1750 2200 1900 1500 2000 1600 2150 2350

An industrial psychologist is investigating the effects of work environment on employee attitudes. A group of20 recently hired sales trainees were randomly assigned to one of four different ?home rooms? - five traineesper room. Each room is identical except for wall color. The four colors used were light green, light blue, grayand red. The psychologist wants to know whether room color has an effect on attitude, and, if so, wants tocompare the mean attitudes of the trainees assigned to the four room colors. At the end of the trainingprogram, the attitude of each trainee was measured on a 60-pt. scale (the lower the score, the poorer theattitude). The data was subjected to a one-way analysis of variance. At ? = 0.05, what would be the bestinterpretation? ONE-WAY ANOVA FOR ATTITUDE BY COLOR SOURCE DF SS MS BETWEEN 3 1678.15 559.3833 59.03782 0.0000 WITHIN 16 151.6 9.475 TOTAL 19 1829.75

True or False: It is required for the Two-Way ANOVA that the populations all have the same variance.

An industrial psychologist is investigating the effects of work environment on employee attitudes. A group of20 recently hired sales trainees were randomly assigned to one of four different ?home rooms? - five traineesper room. Each room is identical except for wall color. The four colors used were light green, light blue, grayand red. The psychologist wants to know whether room color has an effect on attitude, and, if so, wants tocompare the mean attitudes of the trainees assigned to the four room colors. At the end of the trainingprogram, the attitude of each trainee was measured on a 60-pt. scale (the lower the score, the poorer theattitude). The data was subjected to a one-way analysis of variance. Give the null hypothesis for the ANOVA Ftest shown on the printout. ONE-WAY ANOVA FOR ATTITUDE BY COLOR SOURCE DF SS MS BETWEEN 3 1678.15 559.3833 59.03782 0.0000 WITHIN 16 151.6 9.475 TOTAL 19 1829.75

Four different leadership styles (A, B, C, and D) used by Big-Six accountants were investigated. As part of adesigned study, 15 accountants were randomly selected from each of the four leadership style groups (a total of60 accountants). Each accountant was asked to rate the degree to which their subordinates performedsubstandard field work on a 10-point scale -- called the ?substandard work scale?. The objective is to comparethe mean substandard work scales of the four leadership styles. The data on substandard work scales for all 60observations were subjected to an analysis of variance. Interpret the results of the ANOVA test shown on theprintout for ? = 0.05. ONE-WAY ANOVA FOR SUBSTAND BY STYLE SOURCE DF SS MS BETWEEN 3 2800.95 933.650 4.980 0.0039 WITHIN 56 10,498.88 187.480 TOTAL 59 13,299.83

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. Find the teststatistic F to test the hypothesis that there is no difference in the average age of each group. Use α = 0.01. Middle School Teachers High School Teachers College Teachers 23 36 45 28 38 45 27 41 36 37 47 61 52 42 39 25 31 35