Exam 12: Analysis of Variance

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

Assume you are conducting a two-way ANOVA and have found a significant interaction between the two factors.Explain what conclusions you can make from the results and what if any further steps should be taken.

A car company is interested in testing to see whether the mean miles that a car engine will last without changing oil is the same or different depending on which brand of oil is used.The engineers also wish to control for the type of transmission (manual or automatic)that is used.To conduct this test,the car company obtains enough engines so that all four oil brands can be tested in a design that involves no replication.Based on this information,how many engines will be needed to conduct the test?

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:

An Internet service provider is interested in testing to see if there is a difference in the mean weekly connect time for users who come into the service through a dial-up line,DSL,or cable Internet.To test this,the ISP has selected random samples from each category of user and recorded the connect time during a week period.The following data were collected: Based upon these data and a significance level of 0.05,which of the following statements is true?

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.

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 Based on the information provided,should we conclude that the three populations (cities)have equal variances in terms of recreation spending during August? Test at the 0.05 level of significance.

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.

A hotel chain has four hotels in Oregon.The general manager is interested in determining whether the mean length of stay is the same or different for the four hotels.She selects a random sample of n = 20 guests at each hotel and determines the number of nights they stayed.Assuming that she plans to test this using an alpha level equal to 0.05,which of the following is the appropriate alternative hypothesis?

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 degrees of freedom for the MSE in this two-factor ANOVA design is 48.

A test is conducted to compare three difference income tax software packages to determine whether there is any difference in the average time it takes to prepare income tax returns using the three different software packages.Ten different people's income tax returns are done by each of the three software packages and the time is recorded for each.The computer results are shown below. Based on these results and using a 0.05 level of significance which is correct regarding the primary hypothesis?

A personal computer assembly company is interested in studying the time it takes to assemble a computer under different conditions.Specifically,two factors are to be controlled: Factor A (Sample)is the number of individual work stations in the line and Factor B (Columns)is whether the assembly was done on day shift,swing shift,or graveyard shift.The following data were obtained in the study where the response variable is the time required to assemble the PC from start to final test. Carry out the appropriate statistical tests using an alpha equal .05 level.

The general idea is that interaction between two factors means that the effect due to one of the factors is not uniform across all levels of the other factor.

In a one-way analysis of variance test,the following null and alternative hypotheses are appropriate:

In a one-way analysis of variance design,the total variation in the data across the various factor levels can be partitioned into two parts,the within sample variation and the between sample variation.

Considering the following printout for a two-factor ANOVA design,which of the following is a proper conclusion to reach?

In a two-factor ANOVA design with replications,there are three hypotheses to be tested; test for factor A,test for factor B,and test for interaction between factors A and B.

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

A fixed effects analysis of variance differs from a random-effects analysis of variance in the way in which the sums of squares are computed.

A fast food chain operation is interested in determining whether the mean per customer purchase differs by day of the week.To test this,it has selected random samples of customers for each day of the week.The analysts then ran a one-way analysis of variance generating the following output: Anova: Single Factor SUMMARY ANOVA Based upon this output,which of the following statements is true if the test is conducted at the 0.05 level of significance?