Exam 14: Analysis of Variance

Sub Sandwich Customers The marketing manager of a Sub Shop chain is in the process of examining some of the demographic characteristics of her customers.In particular,she would like to investigate the belief that the ages of the customers of Sub Shops,hamburger emporiums,and fast-food chicken restaurants are different.The ages of eight randomly selected customers of each of the restaurants are recorded and listed below.From previous analyses we know that the ages are normally distributed with equal variances for each group. ​ ​ -{Sub Sandwich Customers Narrative} Set up the ANOVA Table.Use α = 0.05 to determine the critical value.

Arthritis Pain Formulas A pharmaceutical manufacturer has been researching new medications formulas to provide quicker relief of arthritis pain.Their laboratories have produced three different medications and they want to determine if the different medications produce different responses.Fifteen people who complained of arthritis pains were recruited for an experiment; five were randomly assigned to each medication.Each person was asked to take the medicine and report the length of time until some relief was felt (minutes).The results are shown below. (Assume normal distributions with equal variances.) ​ ​ -{Arthritis Pain Formulas Narrative} Set up the ANOVA Table.Use α = 0.05 to determine the critical value.

The distribution of the test statistic for analysis of variance is the F-distribution.

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:

In the randomized block design ANOVA,the sum of squares for error equals:

Tukey's multiple comparison method is based on the Studentized range statistic.

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

Motorcycle Repair Cost Motorcycle insurance appraisers examine motorcycles that have been involved in accidental collisions and estimate the cost of repairs.An insurance executive claims that there are significant differences in the estimates from different appraisers.To support his claim he takes a random sample of six motorcycles that have recently been damaged in accidents.Three appraisers then estimate the repair costs of all six motorcycles.The data are shown below. ​ ​ -{Motorcycle Repair Cost Narrative} Set up the ANOVA Table.Use α = 0.05 to determine the critical values.

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. ​ ​ -{Health Inspectors' Ages Narrative} Use Tukey's multiple comparison method to determine which means differ.

Consider the following ANOVA table: The number of treatments is

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

A randomized block design experiment produced the following data. ​ a.Set up the ANOVA Table.Use α = 0.05 to determine the critical values. b.Test to determine whether the treatment means differ.(Use α = 0.05.) c.Test to determine whether the block means differ.(Use α = 0.05.)

In which case can an F-test be used to compare two population means?

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 ____________________ design.

In the two-factor ANOVA where a is the number of factor A levels,b is the number of factor B levels,r is the number of replicates,and n is the total number of observations,the number of degrees of freedom for error is:

Consider the following ANOVA table: The total number of observations is:

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 Narrative} Set up the ANOVA Table.Use α = 0.05 to determine the critical value.

When the variation associated with blocks is removed from the data,SSE increases.

Acid Reflux A partial ANOVA table in a randomized block design is shown below,where the treatments refer to different acid reflux medicines,and the blocks refer to groups of men with similar levels of stomach acid. ​ ​ -{Acid Reflux Narrative} Fill in the missing values (identified by asterisks)in the above ANOVA Table.

Which of the following is true regarding SSB?