Exam 14: Analysis of Variance

Health Inspectors' Ages In order to examine the differences in ages of health inspectors among five counties,a Health Department statistician took random samples of six inspectors' ages in each county.The data are listed below.An F-test using ANOVA showed that average age differs for at least two counties. Ages of hipectors among Five sehoal Districts 1 2 3 4 5 41 39 36 45 53 53 48 28 37 55 28 41 29 46 49 45 51 33 48 56 40 49 27 51 48 59 50 26 49 61 -{Health Inspectors' Ages Narrative} Use Fisher's LSD procedure with $\alpha$ = .05 to determine which population means differ.

To test for interaction between factors A and B in a two-factor ANOVA,you use the F statistic that equals ____________________ divided by ____________________.

SST measures the variation ____________________ treatments.

The number of degrees of freedom for the denominator in one-way ANOVA test involving 4 population means with 15 observations sampled from each population is:

When the problem objective is to compare more than two populations,the experimental design that is the counterpart of the matched pairs experiment is called the randomized block design.

In the randomized block design for ANOVA,where k is the number of treatments and b is the number of blocks,the number of degrees of freedom for error is:

The null hypothesis of ANOVA is that all the population means are ____________________.

In ANOVA the populations are classified according to one or more criterion,called ____________________.

Gold Funds An investor studied the percentage rates of return of three different gold funds.Random samples of percentage rates of return for four periods were taken from each fund.The results appear in the table below: Gold Funds Percentage Rates Fund 1 Fund 2 Fund 3 12 4 9 15 8 3 13 6 5 14 5 7 17 4 4 -{Gold Funds Narrative} Set up the ANOVA Table.Use $\alpha$ = 0.05 to determine the critical value.

GMAT Scores A recent college graduate is in the process of deciding which one of three graduate schools he should apply to.He decides to judge the quality of the schools on the basis of the Graduate Management Admission Test (GMAT)scores of those who are accepted into the school.A random sample of six students in each school produced the following GMAT scores.Assume that the data are normally distributed with equal variances for each school. GMAT SEons School 1 School 2 School 3 650 105 590 620 550 510 630 700 520 580 630 500 710 600 490 690 650 530 -{GMAT Scores Narrative} Set up the ANOVA Table.Use $\alpha$ = 0.05 to determine the critical value.

The analysis of variance (ANOVA)technique analyzes the variance of the data to determine whether differences exist between the population means.

Which of the following is not a required condition for one-way ANOVA?

{TV News Viewing Habits Narrative} Can she infer at the 5% significance level that differences in hours of television watching exist among the three cities?

In a two-factor ANOVA,where a is the number of factor A levels and b is the number of factor B levels,the number of degrees of freedom for the interaction term is

LSAT Scores A recent college graduate is in the process of deciding which one of three Law schools he should apply to.He decides to judge the quality of the schools on the basis of the Law School Admission Test (LSAT)scores of those who are accepted into the school.A random sample of six students in each school produced the following LSAT scores.An F-test using ANOVA concluded that average LSAT scores differ for at least two of the schools. LSAT Scores School 1 School 2 School 3 650 510 590 620 550 510 630 700 520 580 630 500 710 600 490 690 650 530 -{LSAT Scores Narrative} Use Tukey's method with $\alpha$ = 0.05 to determine which population means differ.

Keyboard Configuration and Size The data shown below were taken from a 2 * 3 factorial experiment to examine the effects of factor A (keyboard configuration,3 levels)and factor B (keyboard size,2 levels)on typing speed.Each cell consists of the times needed for each of 4 randomly assigned keyboardists to type a standard document under each set of conditions (in minutes). Factor B Factor A 1 2 1 26 24 19 21 20 20 2 21 23 30 33 24 27 25 31 29 29 26 31 22 23 27 24 17 26 -{Keyboard Configuration and Size Narrative} Test at the 5% significance level to determine if time differences exist among the different keyboard configurations.

SSE measures the variation ____________________ treatments.

When the effect of a level for one factor depends on which level of another factor is present,the most appropriate ANOVA design to use in this situation is the:

The test statistic of the single-factor ANOVA equals:

The primary interest of designing a randomized block experiment is to: