Exam 10: Analysis of Variance: Comparing More Than Two Means

A counselor obtains SAT averages for incoming freshmen each year for a period covering 14 years, with the objective of determining the relationship between the SAT score and the year the test was Given. The averages are then subjected to analysis for the purpose of drawing a conclusion Regarding a trend. Determine whether the study is observational or designed.

An economist is investigating the impact of todayʹs economy on workers in the manufacturing industry who have been laid off. A sample of 50 workers was randomly selected from all workers In manufacturing that have been laid off in the past year. The following variables were measured For each laid off worker: length of time jobless (number of weeks)and tax status (single, married, Or married/head of household). The data for the 50 workers were entered into the computer and Analyzed to determine if the mean number of weeks jobless differed for the three tax status groups. The Tukey multiple comparison printout is shown below: Tukey HSD All-Pairwise Comparisons Test of JOBLESS by STATUS Give the population mean(s) which are in the statistically smallest group.

In an experiment with 10 treatments, how many pairs of means can be compared?

In a study to determine the least amount of time necessary to clean an SUV while maintaining a high quality standard, the owner of a chain of car washes designed an experiment where 20 Employees were divided into four groups, each with five members. Each member of each group Was assigned an SUV to clean within a certain time limit. The time limits for the groups were 20 Minutes, 25 minutes, 30 minutes, and 35 minutes. After the time limits for each group had expired, The owner inspected each SUV and rated the quality of the cleaning job on a scale of 1 to 10. What Are the possible values of the response variable?

A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars)were recorded for a sample of 60 randomly Selected grocery items at each of the three supermarkets. In order to reduce item-to-item Variation, the prices were recorded for each item on the same day at each supermarket. Identify the blocks for this experiment.

The variable measured in the study is called __________.

A multiple-comparison procedure for comparing four treatment means produced the confidence intervals shown below. Rank the means from smallest to largest. Use solid lines to connect those Means which are not significantly different. - :(16,36) - :(7,23) - :(4,20) - :(-18,-4) - :(-20,-8) - :(-9,-2)

An appliance manufacturer is interested in determining whether the brand of laundry detergent used affects the average amount of dirt removed from standard household laundry loads. An Experiment is set up in which 10 laundry loads are randomly assigned to each of four laundry Detergents-Brands A, B, C, and D (a total of 40 loads in the experiment). The amount of dirt Removed, y, (measured in milligrams)for each load is recorded and subjected to an ANOVA Analysis, including a follow-up Tukey analysis. Which of the following inferences concerning the Tukey results below is incorrect? Brands Sample Means B 184 D 172 A 143 C 131

Four brands of baseball bats were tested to determine which bat allowed hitters to hit a baseball farthest. Eight different batters were thrown 25 pitches while hitting with each of the four bats (assigned in random order). The average distance of the five longest hits using each bat is shown In the table below. The goal is to determine if the average hit distance differs for the four brands of Baseball bats. Batter Brand 1 Brand 2 Brand 3 Brand 4 1 307 315 300 275 2 310 317 305 285 3 335 335 330 302 4 325 328 320 300 5 300 305 295 270 6 345 350 340 310 7 312 315 308 300 8 298 302 295 288 The ANOVA table output is shown here: Source DF SS MS F P Batter 7 6227.4 946.77 39.70 0.0000 Brand 3 4117.6 1372.54 57.55 0.0000 Error 21 500.9 23.85 Total 31 11245.9 Based on the p-value for this test, make the proper conclusion about the treatments in this experiment.

An experiment was conducted to compare the mean iron content in iron ore pieces determined by three different methods: (1)mechanical, (2)manual, and (3)laser. Five 1-meter long pieces of iron Ore were removed from a conveyor belt, and the iron content of each piece was determined using Each of the three methods. The data are shown below. How should the data be analyzed?

Find the following: $P ( F \leq 3.29 )$ , for $v _ { 1 } = 5 , v _ { 2 } = 20$

a. Calculate the mean response for each treatment b. The MINITAB ANOVA printout is shown here. Test for interaction at the $\alpha = 0.05$ leve of significance. Analysis of variance for response. Source df SS MS F A 1 0.53777 0.53777 0.11851 B 2 5.02708 2.51334 0.55391 AB 2 13.49334 6.74667 1.48678 Error 6 27.22667 4.53778 Total 11 46.28486 c. Does the result warrant tests of the two factor mean effects?

Suppose an experiment utilizing a random block design has 5 treatments and 11 blocks for a total of 55 observations. Assume that the total Sum of Squares for the response is $\mathrm { SS }$ (Total) $= 400$ . If the Sum of Squares for Treatments (SST) is $30 \%$ of SS(Total), and the Sum of Squares for Blocks (SSB) is $20 \%$ of SS (Total), find the $F$ values for this experiment.

An experiment was conducted using a randomized block design. The data from the experiment are displayed in the following table. TREATMENT BLOCK 1 2 3 1 16 21 14 2 15 24 14 3 18 20 15 Fill in the missing entries for an ANOVA table. SOURCE df SS MS F Treatments 86.22 Blocks Error

Psychologists have found that people are generally reluctant to transmit bad news to their peers. This phenomenon has been named the ʺMUM effect.ʺ To investigate the cause of the MUM effect, 40 undergraduates at a certain university participated in an experiment. Each subject was asked to Administer an IQ test to another student and then provide the test taker with his or her percentile Score. (Unknown to the subject, the test taker was a bogus student who was working with the Researchers.)The experimenters manipulated two factors, subject visibility and success of test Taker, each at two levels. Subject visibility was either visible or not visible to the test taker. Success Of test taker was either top 20% or bottom 20%. Ten subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions, then the time (in seconds)between the end of the test and the Delivery of the percentile score from the subject to the test taker was measured. (This variable is Called the latency to feedback.)The data was subject to an analysis of variance, with the following Results: Source df SS MS F PR > F Subject visibility 1 1380.24 1380.24 4.25 0.430 Test taker success 1 1325.16 1325.16 4.10 0.05 Visibility x success 1 3385.80 3385.80 10.45 .002 Error 36 11,664.00 324.00 Total 39 17,755.20 Which conclusion can you draw from the analysis? Use $\alpha = .01$ .

A multiple-comparison procedure for comparing four treatment means produced the confidence intervals shown below. For each pair of means, indicate which mean is larger or indicate that there Is no significant difference. - :(18,34) - :(7,23) - :(6,18) - :(-17,-5) - :(-22,-6) - :(-13,7)

Four brands of baseball bats were tested to determine which bat allowed hitters to hit a baseball farthest. Eight different batters were thrown 25 pitches while hitting with each of the four bats (assigned in random order). The average distance of the five longest hits using each bat is shown In the table below. The goal is to determine if the average hit distance differs for the four brands of Baseball bats. Batter Brand 1 Brand 2 Brand 3 Brand 4 1 307 315 300 275 2 310 317 305 285 3 335 335 330 302 4 325 328 320 300 5 300 305 295 270 6 345 350 340 310 7 312 315 308 300 8 298 302 295 288 A partial ANOVA table is shown below. Source DF SS MS F Batter 7 946.77 Brand 3 Error 21 500.9 Total 31 11245.9 Find the F-value in the table above for testing whether the average distance hit for the four brands Of baseball bats differ.

A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars)were recorded for a sample of 60 randomly Selected grocery items at each of the three supermarkets. In order to reduce item-to-item Variation, the prices were recorded for each item on the same day at each supermarket. Identify the treatments for this experiment.

Which of the following is not a condition required for a valid ANOVA F-test for a completely randomized experiment?

An industrial psychologist is investigating the effects of work environment on employee attitudes. A group of 20 recently hired sales trainees were randomly assigned to one of four different ʺhome Roomsʺ- five trainees per room. Each room is identical except for wall color. The four colors used Were light green, light blue, gray, and red. The psychologist wants to know whether room color Has an effect on attitude, and, if so, wants to compare the mean attitudes of the trainees assigned to The four room colors. At the end of the training program, the attitude of each trainee was measured On a 60-pt. scale (the lower the score, the poorer the attitude). The data was subjected to a One-way analysis of variance. Give the null hypothesis for the ANOVA F-test shown on the printout.