Download Lesson 12 –Homework 12

Lesson 12 –Homework 12
Notes:
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You may use Minitab when appropriate and include the Minitab output in your homework. To
place Minitab output into your homework, highlight the portion of the Minitab printout you
want, copy that to the clipboard, and then paste it into the document.
Show your work to get full credit.
Homework Problems (Submit to Dropbox for HW 12 by its due day)
1.
(10 pts) A researcher conducts an experiment to examine the relationship between the weight gain of
chickens whose diets had been supplemented by different amounts of amino acid lysine and the
amount of lysine ingested. Since the percentage of lysine is known, and we can monitor the amount of
feed consumed, we can determine the amount of lysine eaten. A random sample of twelve 2-wee-old
chickens was selected for the study. Each was caged separately and was allowed to eat at will from
feed composed of a base supplemented with lysine. The ample data summarizing weight gains and
amounts of lysine eaten over the test period are given below. (In the data, y represents with gain in
grams, and x represents the amount of lysine ingested in grams.)
Chick
y
x
1
14.7
0.09
2
17.8
0.14
3
19.6
0.18
4
18.4
0.15
5
20.5
0.16
6
21.1
0.23
7
17.2
0.11
8
18.7
0.19
9
20.2
0.23
10
16
0.13
11
17.8
0.17
12
19.4
0.21
a) Create a scatterplot of the data. Does a linear model seem appropriate?
b) From the Minitab output below, obtain the estimated linear regression model.
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2.
(25 pts) Refer to problem one to answer the following. (Note that when reporting the p-value, pay
attention to whether this is a one-tailed test or a two tailed test being conducted and the test performed
by the software.)
a) What is the estimate of the model variance, 𝜎𝑒2 ?
b) Identify the standard error of 𝛽̂1
c) Conduct a statistical test of the research hypothesis that for this diet preparation and length of study,
there is a direct (positive) linear relationship between weight gain and amount of lysine eaten.
3.
(20 pts) For the data given in problem one, calculate a 95% interval for the mean response of weight
gain when x=0.22 and a 95% interval for the weight gain of a chick with x=0.22.
4.
(15 pts) Use the regression equation from problem one to predict the weight gain or mean weight gain
of a chick with x=0.84? Explain briefly.
5.
(10 pts) An airline studying fuel usage baa certain type of aircraft obtains data on 12 flights. The air
mileage x in hundreds of miles and the actual fuel use y in gallons. The data and Minitab regression
output is shown below.
2
gallons
miles
470
480
540
650
610
720
600
795
620
890
630
900
700
910
710
820
785
1000
800
1050
800
1150
950
1300
a) Identify the estimated regression equation.
b) What are the sample correlation coefficient and the coefficient of determination? Provide an
interpretation of the coefficient of determination as it relates to this problem.
6.
(20 pts) Refer to problem five. Use software to answer.
a) Predict the mean fuel usage (gallons) of all 1,000-mile flights. Give a 95% confidence interval.
b) Predict the fuel usage (gallons) of a particular 1,000-mile flight and the corresponding 95%
prediction interval. Would the usage of 628 gallons be considered exceptionally low?
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