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Date:
Page 1 of 2
Activity 7.1.3 – Inference Problems on Correlation and Regression
Inference on Population Correlation Coefficients
1. The following tables show the sodium content (in mg per serving) and rating for two random
samples of breakfast cereals.
Sample 1, n = 10
Cereal
Post Natural Raisin Bran
Golden Grahams
Double Chex
Wheaties
Frosted Flakes
Fruit Loops
Honey Nut Cheerios
Apple Cinnamon Cheerios
Fruit & Fiber Dates, Walnuts, and Oats
Corn Chex
Sodium
200
280
190
200
200
125
250
180
160
280
Rating
37.84
23.80
44.33
51.59
31.44
32.21
31.07
29.51
40.92
41.45
Sodium
190
220
180
45
0
0
0
180
15
140
Rating
28.59
46.90
28.74
35.25
68.24
54.85
55.33
29.51
33.98
40.45
Sample 2, n = 10
Cereal
Total Raisin Bran
Crispix
Honey-comb
Golden Crisp
Shredded Wheat
Maypo
Raisin Squares
Apple Cinnamon Cheerios
100% Natural Bran
Cracklin' Oat Bran
For each sample, complete the following steps:
A. Use technology to construct a scatterplot of the sample data.
B. Calculate and interpret the sample correlation coefficient.
C. State the assumed value for the population correlation coefficient to conduct a
randomization test.
D. Construct a randomization distribution of sample correlation coefficients (using Statkey).
E. Find the probability of observing a sample correlation coefficient as extreme as the one
found.
F. State whether the observed sample correlation coefficient is statistically significant.
G. State a conclusion about the population correlation coefficient.
Activity 7.1.3
Connecticut Core Algebra 2 Curriculum Version 3.0
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Page 2 of 2
Inference on Population Regression Line Slopes
2. The following table shows the number of cellular phone subscriptions in 2011 (per 100
people) and the average life expectancy in 2011 for a random sample of 10 countries.
Random Sample of 10 Countries
Country
Spain
Brazil
Panama
Russia
Romania
Angola
Ethiopia
Mongolia
Nigeria
United States
Number of Cellular
Subscriptions in 2011
2011 Life Expectancy
(in years)
114
123
204
179
109
48
17
105
59
106
82
75
77
69
75
66
62
64
59
79
Complete the following steps:
A. Use technology to construct a scatterplot of the sample data.
B. Calculate the slope and y-intercept of the least-squares regression line.
C. State the assumed value for the population regression line slope to conduct a
randomization test.
D. Construct a randomization distribution of sample regression lines slopes (using Statkey).
E. Find the probability of observing a sample regression line slope as extreme as the one
found.
F. State whether the observed sample regression line slope is statistically significant.
G. State a conclusion about the population regression line slope.
Activity 7.1.3
Connecticut Core Algebra 2 Curriculum Version 3.0