MAT 210 ASSIGNMENT 3: "ANOVA, One & Two"

This assignment assesses your comprehension and application of the methods shown in Chapters 11 and 12 and the content of the Chapter 12 "add-on." Type all answers on these pages. You may use mathematical characters, if you wish

1. (5) Below is a one-way ANOVA table for three diet programs. One plan uses low fat foods, a second uses rigorous exercise, and a third uses a combination of low fat foods and an exercise regimen.

1. (3) Fill in the question marks in the table above.
2. (2) The critical value for a 5% risk for (since is not in the table) is 3.32.

H0: ; H1: not all sample means are equal.

Compare the test statistic F in the table above with the CV in part (b), what do you think about the effectiveness of this program? Should follow up tests be conducted? Explain.

2. (10) An advertising agency prepares three different commercials for a new outdoor grill. One commercial shows a man cooking, another shows a woman cooking, and a third shows a family enjoying food that has just been prepared on the grill. To determine whether the commercials are equally effective, 10 participants rate the commercials on a set of questions, whose ratings range from 0 to 30. At the 5% level of risk, test whether the three commercials are equally effective for satisfaction. Use Excel for processing.

2. (cont’d)

1. (5) Paste your Excel printout here or attach it to this assignment.
2. (5) Analyze the results in terms of the F critical value and the obtained F. Explain whether all three commercials would be equally effective in mean satisfaction based on the sample means for satisfaction. Do follow up tests need to be conducted to determine which commercial is most effective or least effective?
   3. (10) The director of an income tax agency hires four college students, who are business majors, to help prepare taxes during the busy season. To see whether he should hire any of them for the next year, he samples how long it takes each new employee to prepare similar tax returns for 10 randomly selected customers. Below is a table of their preparation times in minutes. Process the data by Excel at the 5% level of risk.

   Tax Return	Bob	Martha	Paul	Jane
   1	25	30	48	35
   2	60	28	40	21
   3	28	32	35	30
   4	39	28	32	40
   5	26	45	25	75
   6	42	33	49	18
   7	29	41	30	42
   8	62	49	70	83
   9	17	25	15	24
   10	48	19	75	25

   1. (5) Post your Excel printout here or attach it to this assignment.
   2. (5) Assume that all returns have been correctly processed. Analyze the results. Are all four students, on average, equally efficient? Explain by using salient values on your Excel sheet.

4. (10) The owner of Happy Horses Farm owns four young race horses and wants to select the fastest to run in the Kentucky Derby. He designates three jockeys to ride the horses on four similar tracks at his large farm. Below are the times in seconds for riders and horses to run a simulated race.

Process the data on Excel. Use the two-way ANOVA program without replication. This model is used when each cell has only one entry.

1. (5) Paste your printout here, or attach it to this assignment.
2. (5) Address the main effects, for which there are two, one for jockey and the other for horse. There is no interaction with this model. Look on your printout for a high obtained F ratio that is accompanied by a very low P-value. Do you see a high obtained F and a low P-value? If so, where?

5. (5) Below is a copy of an Excel report for a two-way ANOVA with replication run. Read the printout and answer the questions.

ANOVA

1. (2) If Sample is the first independent variable and Columns is the second independent variable, are either one significant? If so, identify which one based on evidence.
2. (2) How many values are in each cell? Explain.
3. (1) Is there an interaction between variables? Explain with evidence.

6. (10)

Problem : A researcher wants to determine how productive males and females are when working with machines of varying weights. His first hypothesis is that there is no difference between males and females in the number of teddy bears they can produce in a typical 8-hour shift. His second hypothesis is that the weight of machinery used makes no difference on productivity. His third hypothesis is that there is no interaction between gender and weight of a processing machine.

Assume that he has controlled all other variables that could interact with the two designated independent variables. Among these variables are age, working experience, factory conditions, and type of product. In other words, all teddy bears are the same size. Further assume that the 30 participants have been chosen at random after age and experience were controlled.

Below are the data that you should input to Excel’s two-way ANOVA with replication program.

The Toy Factory Problem

1. (5) Paste your Excel printout here, or attach it to this assignment.

   Anova: Two-Factor With Replication
   SUMMARY	Light Wt	Mid Wt	Heavy Wt	Total
   male
   Count	5	5	5	15
   Sum	93	202	317	612
   Average	18.6	40.4	63.4	40.8
   Variance	4.3	4.3	37.3	371.6
   female
   Count	5	5	5	15
   Sum	306	195	93	594
   Average	61.2	39	18.6	39.6
   Variance	48.7	2.5	17.3	343.8285714
   Total
   Count	10	10	10
   Sum	399	397	410
   Average	39.9	39.7	41
   Variance	527.6555556	3.566666667	581.7777778
   ANOVA
   Source of Variation	SS	df	MS	F	P-value	F crit
   Sample	10.8	1	10.8	0.566433566	0.458999	4.259675
   Columns	9.8	2	4.9	0.256993007	0.775475	3.402832
   Interaction	9548.6	2	4774.3	250.4003497	8.37E-17	3.402832
   Within	457.6	24	19.06666667
   Total	10026.8	29

2. (5) Analyze the Excel report and discuss the findings. What would you do if you were a manager at that toy factory?

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