10. If an experiment is conducted with 5 conditions and 6 subjects in each condition, what are dfn and dfe?
17. The following data are from a hypothetical study on the effects of age and time on scores on a test of reading comprehension. Compute the analysis of variance summary table.
12-year-olds
16-year-olds
30 minutes
66
74
68
71
59
67
72
82
46
76
60 minutes
69
95
61
92
69
95
73
98
61
94
Illowsky – Ch. 13
Use the following information to answer the next three exercises. Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses.
Northeast
South
West
Central
East
16.3
16.9
16.4
16.2
17.1
16.1
16.5
16.5
16.6
17.2
16.4
16.4
16.6
16.5
16.6
16.5
16.2
16.1
16.4
16.8
x-bar =
________
________
________
________
________
s^2 =
________
________
________
________
________
H0:µ1=µ2=µ3=µ4=µ5
Hα: At least any two of the group meansµ1,µ2, …,µ5are not equal.
61. degrees of freedom – numerator: df(num) = ________
63. F static = ________
69. A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same. Suppose that Table 13.24 shows the results of a study.
CNN FOX Local
45 15 72
12 43 37
18 68 56
38 50 60
23 31 51
35 22 ?
Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.
71. Are the mean number of times a month a person eats out the same for whites, blacks, Hispanics and Asians? Suppose that Table 13.26 shows the results of a study.
White
Black
Hispanic
Asian
6
4
7
8
8
1
3
3
2
5
5
5
4
2
4
1
6
6
7
77. A grassroots group opposed to a proposed increase in the gas tax claimed that the increase would hurt working-class people the most, since they commute the farthest to work. Suppose that the group randomly surveyed 24 individuals and asked them their daily one-way commuting mileage. The results are as follows.
Working-Class
Professional (middles incomes)
Professional (wealthy)
17.8
16.5
8.5
26.7
17.4
6.3
49.4
22
4.6
9.4
7.4
12.6
65.4
9.4
11
47.1
2.1
28.6
19.5
6.4
15.4
51.2
13.9
9.3
Determine whether or not the variance in mileage driven is statistically the same among the working class and professional (middle income) groups. Use a 5% significance level.
81. Is the variance for the amount of money, in dollars, that shoppers spend on Saturdays at the mall the same as the variance for the amount of money that shoppers spend on Sundays at the mall? Suppose that the Table 13.34 shows the results of a study.
Saturday
Sunday
Saturday
Sunday
75
44
62
137
18
58
0
82
150
61
124
39
94
19
50
127
62
99
31
141
73
60
118
73
89
STAT 200 Week 7 Homework
a. What would be the predicted score for a person scoring 6 on X?
b. If someone’s predicted score was 14, what was this person’s score on X?
6. For the X,Y data below, compute:
a. r and determine if it is significantly different from zero.
b. the slope of the regression line and test if it differs significantly from zero.
c. the 95% confidence interval for the slope.
X
Y
4
6
3
7
5
12
11
17
10
9
14
21
Lane – Ch. 17
5. At a school pep rally, a group of sophomore students organized a free raffle for
prizes. They claim that they put the names of all of the students in the school in
the basket and that they randomly drew 36 names out of this basket. Of the prize
winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were
seniors. The results do not seem that random to you. You think it is a little fishy
that sophomores organized the raffle and also won the most prizes. Your school is
composed of 30% freshmen, 25% sophomores, 25% juniors, and 20% seniors.
a. What are the expected frequencies of winners from each class?
b. Conduct a significance test to determine whether the winners of the prizes
were distributed throughout the classes as would be expected based on the
percentage of students in each group. Report your Chi Square and p values.
c. What do you conclude?
14. A geologist collects hand-specimen sized pieces of limestone from a particular
area. A qualitative assessment of both texture and color is made with the
following results. Is there evidence of association between color and texture for
these limestones? Explain your answer.
COLOR
COLOR
COLOR
Texture
Light
Medium
Dark
Fine
4
20
8
Medium
5
23
12
Coarse
21
23
4
Illowsky – Ch. 11
True or False
70. The standard deviation of the chi-square distribution is twice the mean.
102. Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place is shown in Table 11.55. Conduct a test for homogeneity at a 5% level of significance.
French Toast
Pancakes
Waffles
Omelettes
Men
47
35
28
53
Women
65
59
55
60
Use the following information to answer the next twelve exercises: Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.
113. df= _______
117. Let a = 0.05
Decision: _______
Conclusion (write out in a complete sentence): _________
The Regression Equation
66. Can a coefficient of determination be negative? Why or why not?
82. The cost of a leading liquid laundry detergent in different
sizes is given in Table 12.31.
Size (ounces)
Cost ($)
Cost per ounce
16
3.99
32
4.99
64
5.99
100
10.99
a. Using “size” as the independent variable and “cost” as the dependent variable, draw a scatter plot.
b. Does it appear from inspection that there is a relationship between the variables? Why or why not?
c. Calculate the least-squares line. Put the equation in the form of:ŷ=a+bx
d. Find the correlation coefficient. Is it significant?
e. If the laundry detergent were sold in a 40-ounce size, find the estimated cost.
f. If the laundry detergent were sold in a 90-ounce size, find the estimated cost.
g. Does it appear that a line is the best way to fit the data? Why or why not?
h. Are there any outliers in the given data?
i. Is the least-squares line valid for predicting what a 300-ounce size of the laundry detergent would you cost? Why or why not?
j. What is the slope of the least-squares (best-fit) line? Interpret the slope
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