Exam 12: Analysis of Variance

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.

Damage to homes caused by burst piping can be expensive to repair.By the time the leak is discovered,hundreds of gallons of water may have already flooded the home.Automatic shutoff valves can prevent extensive water damage from plumbing failures.The valves contain sensors that cut off water flow in the event of a leak,thereby preventing flooding.One important characteristic is the time (in milliseconds)required for the sensor to detect the water leak.Sample data obtained for four different shutoff valves are contained in the file entitled Waterflow. Produce the relevant ANOVA table and conduct a hypothesis test to determine if the mean detection time differs among the four shutoff valve models.Use a significance level of 0.05.

A national car rental agency is interested in determining whether the mean days that customers rent cars is the same between three of its major cities.The following data reflect the number of days people rented a car for a sample of people in each of three cities.Given this information,the correct null and alternative hypotheses are: H₀ : ₁ = ₂ = ₃ H_a : not all _j are equal.

To test for the stopping distances of four brake systems,10 of the same make and model of car are selected randomly and then are assigned randomly to each of four brake systems.This is a randomized complete 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 a significance level of 0.05 and these sample data,test to determine whether blocking was necessary in this example.Use a test-statistic approach.

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.

What are the assumptions for a one-way analysis of variance design?

In conducing one-way analysis of variance,the population distributions are assumed normally distributed.

A golf ball manufacturer has three dimple patterns it is interested in analyzing to see whether one results in longer driving distances.However,it also wishes to control for the cover material the ball is made from since it believes that the material might affect driving distance.Four materials can be used.The following data represent the results of tests in which each combination of dimple pattern and cover material were used and the length of the ball hit by a robot has been recorded.The test will be conducted using an alpha = 0.05 level. Given these data,which of the following statements is true?

A national car rental company recently conducted a study recently in which cars with automatic and standard transmissions (factor A-Sample)were rented to male and female customers (factor B-Columns).Three customers in each category were randomly selected and the miles driven per day was recorded as follows: Based on the design of this study,how many degrees of freedom will be associated with the mean square for factor A?

A start-up cell phone applications company is interested in determining whether house-hold incomes are different for subscribers to three different service providers.A random sample of 25 subscribers to each of the three service providers was taken,and the annual household income for each subscriber was recorded.The partially completed ANOVA table for the analysis is shown here: Complete the ANOVA table by filling in the missing sums of squares,the degrees of freedom for each source,the mean square,and the calculated F-test statistic.

A study recently conducted by a marketing firm analyzed three different advertising designs (factor A)and four different income levels (factor B)of potential customers.At each combination of factor A and factor B,5 customers are observed and the number of products produced is recorded.Interaction between the two factors would exist if low income customers have higher mean buying when design 1 is used,but higher income customers have higher mean buying when designs 2 and 3 are used.

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.

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 mean spending during August? Test at the 0.05 level of significance.

Which of the following is an assumption for the one-way analysis of variance experimental design?

Which type of ANOVA can include interaction?

Given the partially completed ANOVA table below,the test statistic for determining if there is any blocking effect is F = 4.38.

A golf ball manufacturer has three dimple patterns it is interested in analyzing to see whether one results in longer driving distances.However,it also wishes to control for the material the ball is made from since it believes that the material might affect driving distance.Four materials can be used.The following data represent the results of tests in which each combination of dimple pattern and cover material were used and the length of the ball hit by a robot has been recorded.The test will be conducted using an alpha = 0.05 level. Given these data,what is the value of Fisher's Least Significant Difference critical value?

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: Based on these sample results and a significance level equal to 0.05,assuming that the null hypothesis of equal means has been rejected,the Tukey-Kramer critical range is: