BIA 654 Midterm Exam, Fall 2019

BIA代写 Johan would like to make a hypothesis test. Assume that the observations in each group come from a normal distribution.

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  1. Johan has heard that cows produce more milk when they get to listen to classical music.BIA代写

He sets up an experiment to test this, where he randomly selects 6 cows, from his 12 cows, which get to listen to classical music, and the rest 6 that do not. The resulting milk production over a week is then measured for each cow:

Cows listening to classical music 113 118 126 121 111 119
Cows with no music 110 116 110 121 117 110

 

 

 

 

 

Some computations and numbers that might be useful for you to save time:

(113+118+ 126 + … + 119)/6 = 118, (110+116+ 110 + … + 110)/6 = 114

(113-118)^2 + (118-118) ^2 + … + (119-118) ^2 = 148 (This will be useful in computing a sample variance.)

(110-114)^2 + (116-114) ^2 + … + (110-114) ^2 = 110

t(0.025, df=10) = 2.228, t(0.05, df=10) = 1.812, t(0.1, df=10) = 1.372,  t(0.025, df=12) = 2.179, t(0.05, df=12) = 1.782

a) Johan would like to make a hypothesis test. Assume that the observations in each group come from a normal distribution.BIA代写

Assume also that the population variances of two groups are the same (say, from an F-test). State hypotheses, choose a test, and carry it out with significance level 5%. How would you conclude? Do you have to make additional assumptions in order to use your test? (10 points)BIA代写

b) Find a 90% confidence interval for the difference between the expected milk production with and without music. 
(10 points)
c) Johan would like to study the question further, so he takes the music away from the cows that had been listening, and instead lets the other six cows listen to the music for a week.BIA代写

This gives him 12 new measurements. How can he analyze his new and old data together? Describe with formulas how to do the computations. Why is he likely to get a better result this time? (10 points)BIA代写

d) Assume Johan wanted to find out whether the musical style mattered.

He selects 5 different musical styles, and performs a new experiment lasting 5 weeks, where each cow gets to listen to one week of each type of music, whereafter its milk production for that week is measured. Assume Johan already know from his past experiences that there is an individual variation from cow to cow in milk production. What kind of analysis method could he use on the resulting data? (It is enough to describe the method in one sentence.) (10 points)BIA代写

       2. Rick is comparing the effect of three different typesof running shoes on his running time.

He has made, in a randomized order, 5 test runs with each type of running shoes. He would like to test his null hypothesis that the running shoes do not influence his running times.BIA代写

           a) What is a factor? How many levels are there?  (10 points)
           b)He has started to fill out the ANOVA table below for his data analysis.

Making the usual normal population and independent sample assumptions, complete the table and test for Rick’s  null hypothesis with significance level 5%. 
(10 points)BIA代写

Source of

Variation

Sum of squares Degrees of freedom Mean sum

of squares

Test statistic
Between Groups 213      
Within

Groups

(Errors)

       
Total 432      

 

 

 

 

 

 

 

 

 

 

 

* Use the fact that F(2, 12; 0.05) = 3.89, F(3, 12; 0.05) = 3.49, F(3, 14; 0.05) = 3.34.

 

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  1. Karen Donegan, a staffer at the business school, is thinking about buying some new golf equipment to improve her game in preparation for the annual golf tournament.BIA代写

One day she comes across some notes on experimental design that she finds on top of a file cabinet near her office. “Hmm,” she thinks to herself as she begins to read them, “this looks interesting. Maybe this will help me decide what equipment to purchase.”BIA代写

Karen has been thinking about replacing her current steel shaft, small head driver.

The company that makes her clubs has three other drivers that she is considering. The first has the same steel shaft but a newly designed very large head. The second has a graphite shaft with the same small head that is on her current driver, while the third has the graphite shaft with the newly designed very large head. She is also wondering whether a new pair of golf shoes might help, as well as switching to an expensive golf ball (at $3.00 per ball) rather than sticking with her discount store special (at $0.75 per ball).BIA代写

She also has her eye on a rather expensive new golf sweater, which should put her in the right frame of mind to hit some really long drives.

Finally, she does not wear a golf glove when she plays, and her husband pointed out to her that she is no Fred Couples, one of the few golf professionals who does not wear a glove. After spending an evening reading the notes, Karen concludes that “this is pretty clear” and decides to perform the experiment whose design matrix is shown below. She includes six factors and decides to do 16 runs, all to be performed at the local driving range. Each run is performed in random order.BIA代写

Karen buys the necessary golf balls, and the glove but is able to borrow the shoes and golf clubs from a local store. She has her own steel shaft, small-head driver, and she has ten days to return the sweater for a full refund.BIA代写

The design matrix and the results of the experiment are shown below. Each run is a single drive (shot) and the response variable is the distance the shot carries in yards. Karen’s goal is to find the equipment that will maximize her distance, but she doesn’t want to spend money on anything that will not help in that regard.BIA代写

a) Obtain the estimated effects and determine the confounding patterns (you can use stat packages or hand calculations).

Assume interactions of order 3 or higher are negligible (hence no need to determine their confounding patterns). (7 points)BIA代写

b) Find all the effects including higher-order interactions that are confounded with C, with CD, with AB. (5 points)
c) Suppose that based on prior extensiveexperience (that is, based on large number of repetitions) at the driving range measuring the length of her drives, Karen has determined that the standard deviation of a single drive is 13 yards.

What is the 95% confidence interval for an effect? Which effects are significant? (7 points)BIA代写

d) Based on your analysis of the results, what are the most reasonable and likely conclusions you can draw without doing any additional runs?

What should Karen do? Make plots for effects of A and B and their interaction. What is the regression prediction equation? (7 points)BIA代写

e) How much additionalyardage can Karen expect to get if she follows your advice? (7 points)
f) Suppose instead of doing all 16 runs on one day, Karen decides to do 8 of the runs on

one day and the other 8 runs the next day. Karen’s husband Harold suggests she do the even numbered runs on one day and the odd numbered runs on the other. Is this a good idea? Explain. A professor at the business school suggests she do runs 1, 3, 6, 8, 10, 12, 13, and 15 on one day and the others on the next day. Karen asks why? The professor says, “Look at the column of signs for the ACD interaction. The runs with – signs should be run on one day and the runs with + signs should be run on the other day. That’s how I picked the runs for each day.” Explain why the professor’s suggestion is better than Harold’s. Think of the day as the “seventh factor” (and see its confounding). (7 points)BIA代写

Factors   Levels
  +
A small club head large club head
B steel shaft graphite shaft
C cheap ball expensive ball
D no glove glove
E old shoes new shoes
F old sweater expensive new sweater

 

 

 

 

 

 

 

 

 

 

 

 

 

  Design with generators: E = ABC, F = BCD    
Run A B C D E F Response
1 182
2 + + 157
3 + + + 155
4 + + + 226
5 + + + 184
6 + + + 166
7 + + 177
8 + + + + 218
9 + + 178
10 + + + + 152
11 + + + 135
12 + + + 232
13 + + + 173
14 + + + 156
15 + + + + 154
16 + + + + + + 223

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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