The questions below are due on the assigned date announced in class and posted o
ID: 3155760 • Letter: T
Question
The questions below are due on the assigned date announced in class and posted on Moodle. Answers should be submitted on a separate sheet of paper. Points are awarded for partial credit for most questions. You must show work to receive these points and all work must be legible. These questions are worth 20 points.
Material Covered: Experimental Design and ANOVA
Homework (20 points):
1. (5 points) Designing medication packaging that resists opening by children, but yields readily to adults, present numerous challenges. In the article “Painful Design” (American Scientist, Vol. 93, Nov. 2, pp 113-118) H. Petroski examined the packaging used for Aleve, a brand of pain reliever. Three new container designs were given to a panel of children aged 42 months to 51 months. For each design, the children were handed the bottle, shown how to open it, and then left alone with it. If more than 20% of the children succeeded in opening the bottle on their own within 10 minutes, even if by using their teeth, the bottle failed to qualify as a child resistant. Identify:
a. experimental units b. response variable c. factor(s)
d. levels of factors
e. treatments
2. (5 points) An experiment is to be conducted to compare four brands of gasoline for gas mileage.
a. Suppose that you randomly divide 24 cars into four groups of 6 cars each and then randomly assign the four groups to the four brands of gasoline, one group per brand. Is this experimental design a completely randomized design or a randomized block design? If is the latter, what are the blocks?
b. Suppose, instead, that you use six different models of cards whose varying characteristics (e.g. weight and horsepower) affect gas mileage. Four cars of each model are randomly assigned to the four different brands of gasoline. Is this experimental design a completely randomized design or a randomized block design? If it is the latter, what are the blocks?
c. Which design is better, the one in part (a) or the one in part (b)
3. (2 points) An F-curve has df = (15, 5). In each case, find the F-value having the specified area to its right.
a. 0.01 b. 0.005
4. (3 points) State the four assumptions required for one-way ANOVA. How crucial are these assumptions.
MATH 282 Spring 2016 Homework 8
5. (5 points) Movie fans use the annual Leonard Martin Movie Guide for facts, cast members, and reviews of 21,000 films. The movies are rated from 4 stars (4*), indicating a very good movie, to 1 star (1*), which Leonard Martin refers to as a “bomb.” The table below gives the running times, in minutes, of a random sample of films listed in one year’s guide. At the 1% significance level, do the data provide sufficient evidence to conclude that a different exists in mean running times among films in the four groups? (Note: T1 = 483, T2 = 573, T3 = 576, T4 = 691, and x2 = 232,117)
1* or 1.5*
2* or 2.5*
3* or 3.5*
4*
75
97
101
101
95
70
89
135
84
105
97
93
86
119
103
117
58
87
86
126
85
95
100
119
1* or 1.5*
2* or 2.5*
3* or 3.5*
4*
75
97
101
101
95
70
89
135
84
105
97
93
86
119
103
117
58
87
86
126
85
95
100
119
Explanation / Answer
3.
An F-curve has df = (15, 5). In each case, find the F-value having the specified area to its right.
a. 0.01 b. 0.005
(a)
In this case,=0.01, the degrees of freedom for the numerator is 15, and the degrees of freedom for the
denominator is 5.
=FINV(0.01,15,5)
=9.7222
(b)
In this case,=0.005, the degrees of freedom for the numerator is 15, and the degrees of freedom for the
denominator is 5.
=FINV(0.005,15,5)
=13.1463
4.
State the four assumptions required for one-way ANOVA
Assumptions:
1.
(a) Experimental units is the childrens are in pannel
(b) response variable is handel the bottel
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