Exam 12: Analysis of Variance

In a one-way ANOVA,which of the following is true?

The State Transportation Department is thinking of changing its speed limit signs.It is considering two new options in addition to the existing sign design.At question is whether the three sign designs will produce the same mean speed.To test this,the department has conducted a limited test in which a stretch of roadway was selected.With the original signs up,a random sample of 30 cars was selected and the speeds were measured.Then,on different days,the two new designs were installed,30 cars each day were sampled,and their speeds were recorded.Suppose that the following summary statistics were computed based on the data: The appropriate test to conduct to determine if the population means are equal is:

In conducting a one-way analysis of variance,if the null hypothesis is true then the variance between groups (MSB)should be approximately equal to the variance within groups (MSW).

To test the mileage efficiency of three new car models,random samples of various sample sizes were selected from each of the three cars and the mpg data obtained are shown below. Based on the sample date,one can conclude that

In a two-factor ANOVA study,if the two factors do not interact,then neither factor A nor factor B can be considered statistically significant.

A study recently conducted by a marketing firm analyzed three different advertising designs and four different income levels of potential customers.At each combination of factor A and factor B,5 customers are observed and the number of products produced are recorded.The total number of degrees of freedom associated with this two-factor ANOVA design is 59.

The term one-way analysis of variance refers to the fact that in conducting the test,there is only one way to set up the null and alternative hypotheses.

Which of the following is NOT one of the assumptions required by the randomized block design?

In a local community there are three grocery chain stores.The three have been carrying out a spirited advertising campaign in which each claims to have the lowest prices.A local news station recently sent a reporter to the three stores to check prices on several items.She found that for certain items each store had the lowest price.This survey didn't really answer the question for consumers.Thus,the station set up a test in which 20 shoppers were given different lists of grocery items and were sent to each of the three chain stores.The sales receipts from each of the three stores are recorded in the data file Groceries. Based on the sample data,which store has the highest average prices? Use Fisher's LSD test if appropriate.

When the world's largest retailer,Walmart,decided to enter the grocery marketplace in a big way with its "Super Stores," it changed the retail grocery landscape in a major way.The other major chains such as Albertsons have struggled to stay competitive.In addition,regional discounters such as WINCO in the western United States have made it difficult for the traditional grocery chains.Recently,a study was conducted in which a "market basket" of products was selected at random from those items offered in three stores in Boise,Idaho: Walmart,Winco,and Albertsons.At issue was whether the mean prices at the three stores are equal or whether there is a difference in prices.The sample data are in the data file called Food Price Comparisons.Using an alpha level equal to 0.05,test to determine whether the three stores have equal population mean prices.If you conclude that there are differences in the mean prices,perform the appropriate posttest to determine which stores have different means.

Three brands of running shoes are each tested by 10 different runners.The amount of wear on the sole of the shoes is then measured.The objective is to determine if there is any difference among the three brands of shoes based on how long the soles last.The degrees of freedom for testing whether there is any blocking effect D₁ = 9 and D₂ = 18.

As a step in establishing its rates,an automobile insurance company is interested in determining whether there is a difference in the mean highway speeds that drivers of different age groups drive.To help answer this question,it has selected a random sample of drivers in three age categories: under 21,21-50,and over 50.The engineers then recorded the drivers' speeds at a designated point on a highway in the state.The subjects were unaware that their speed was being recorded.The following one-way ANOVA output was generated from the sample data.Based upon this output,if the significance level is 0.05,the engineers should conclude that the mean speeds may all be equal since the p-value is less than alpha. ANOVA: Single Factor

In conjunction with the housing foreclosure crisis of 2009,many economists expressed increasing concern about the level of credit card debt and efforts of banks to raise interest rates on these cards.The banks claimed the increases were justified.A Senate subcommittee decided to determine if the average credit card balance depends on the type of credit card used.Under consideration are Visa,MasterCard,Discover,and American Express.The sample sizes to be used for each level are 25,25,26,and 23,respectively. State the number of degrees of freedom available for determining the between-samples variation.

A company has established an experiment with its production process in which three temperature settings are used and five elapsed times are used for each setting.The company then produces one product under each and measures the resulting strength of the product.The managers are mainly interested in determining whether the mean strength is the same at all temperature settings,but they know that controlling for process time is important.The following data were observed from the experiment: Based on these data and experimental design,for a significance level of 0.05,the managers should conclude that they were justified in blocking on the basis of processing time.

A two-factor analysis of variance is conducted to test the effect the price and advertising have on sales of a particular brand of bottled water.Each week a combination of particular levels of price and advertising are used and the sales level is recorded.The computer results are shown below. ANOVA Based on the results above,which of the following is correct?

In order to analyze any potential interactions between factors in an analysis of variance study,it is necessary to have at least two measurements at each level of each factor.

Consider the following: Test to determine whether blocking is effective using an alpha level equal to 0.05

A two-factor analysis of variance is conducted to test the effect that price and advertising have on sales of a particular brand of bottled water.Each week a combination of particular levels of price and advertising are used and the sales amount is recorded.The computer results are shown below. ANOVA Based on the results above and a 0.05 level of significance,which of the following is correct?

In a two-factor ANOVA design,the variances of the populations are assumed to be equal unless there is interaction present.

A study has been conducted to determine whether the mean spending for recreational activities during the month of August differs for residents of three cities.Random samples of 30 people were selected from each city and their spending on recreation was recorded during August.The following output was generated using Excel: ANOVA: Single Factor SUMMARY ANOVA The Excel output shows that the null hypothesis of equal means should be rejected.Given this,perform the appropriate method for determining which population means are different.Conduct the test using an alpha = 0.05 level.