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The data in the table to the right represent the calories and sugar​ (in grams) in one serving of seven different types of breakfast cereals.   a. Compute and interpret the coefficient of​ correlation, r. b. At the 0.05 level of​ significance, is there a significant linear relationship between calories and​ sugar?   Product    Calories    Sugar Cereal 1    84    6 Cereal 2    101    2 Cereal 3    96    4 Cereal 4    113    3 Cereal 5    128    5 Cereal 6    186    10 Cereal 7    204    10                     a. The coefficient of​ correlation, r=enter your response here​, indicates________correlation. ​(Round to three decimal places as​ needed.)   b. Determine the hypotheses for the test. Choose the correct answer below.     A. H Subscript 0​:ρ≤0 H Subscript 1​:ρ>0   B. H Subscript 0​: β Subscript 1≤0 H Subscript 1​: β Subscript 1>0   C. H Subscript 0​: ρ=0 H Subscript 1​: ρ≠0   D. H Subscript 0​: β Subscript 0=0 H Subscript 1​: β Subscript 0≠0   E. H Subscript 0​:ρ≥0 H Subscript 1​:ρ<0   F. H Subscript 0​:β Subscript 1≥0 H Subscript 1​:β Subscript 1<0 Part 3 Compute the test statistic.   The test statistic is______enter your response here. ​(Round to two decimal places as​ needed.) Determine the​ p-value. The​ p-value is enter your response here. ​(Round to three decimal places as​ needed.)   Reach a decision.   ▼  Reject Do not reject H Subscript 0. There is ▼  insufficient sufficient evidence at the 0.05 level of significance to conclude that there is a significant linear relationship between calories and sugar.

The data in the table to the right represent the calories and sugar​ (in grams) in one serving of seven different types of breakfast cereals.   a. Compute and interpret the coefficient of​ correlation, r. b. At the 0.05 level of​ significance, is there a significant linear relationship between calories and​ sugar?   Product    Calories    Sugar Cereal 1    84    6 Cereal 2    101    2 Cereal 3    96    4 Cereal 4    113    3 Cereal 5    128    5 Cereal 6    186    10 Cereal 7    204    10                     a. The coefficient of​ correlation, r=enter your response here​, indicates________correlation. ​(Round to three decimal places as​ needed.)   b. Determine the hypotheses for the test. Choose the correct answer below.     A. H Subscript 0​:ρ≤0 H Subscript 1​:ρ>0   B. H Subscript 0​: β Subscript 1≤0 H Subscript 1​: β Subscript 1>0   C. H Subscript 0​: ρ=0 H Subscript 1​: ρ≠0   D. H Subscript 0​: β Subscript 0=0 H Subscript 1​: β Subscript 0≠0   E. H Subscript 0​:ρ≥0 H Subscript 1​:ρ<0   F. H Subscript 0​:β Subscript 1≥0 H Subscript 1​:β Subscript 1<0 Part 3 Compute the test statistic.   The test statistic is______enter your response here. ​(Round to two decimal places as​ needed.) Determine the​ p-value. The​ p-value is enter your response here. ​(Round to three decimal places as​ needed.)   Reach a decision.   ▼  Reject Do not reject H Subscript 0. There is ▼  insufficient sufficient evidence at the 0.05 level of significance to conclude that there is a significant linear relationship between calories and sugar.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 15PPS
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Question
The data in the table to the right represent the calories and sugar​ (in grams) in one serving of seven different types of breakfast cereals.
 
a. Compute and interpret the coefficient of​ correlation, r.
b. At the 0.05 level of​ significance, is there a significant linear relationship between calories and​ sugar?
 
Product    Calories    Sugar
Cereal 1    84    6
Cereal 2    101    2
Cereal 3    96    4
Cereal 4    113    3
Cereal 5    128    5
Cereal 6    186    10
Cereal 7    204    10                    
a. The coefficient of​ correlation,
r=enter your response here​,
indicates________correlation.
​(Round to three decimal places as​ needed.)
 
b. Determine the hypotheses for the test. Choose the correct answer below.
 
 
A.
H Subscript 0​:ρ≤0
H Subscript 1​:ρ>0
 
B.
H Subscript 0​: β Subscript 1≤0
H Subscript 1​: β Subscript 1>0
 
C.
H Subscript 0​: ρ=0
H Subscript 1​: ρ≠0
 
D.
H Subscript 0​: β Subscript 0=0
H Subscript 1​: β Subscript 0≠0
 
E.
H Subscript 0​:ρ≥0
H Subscript 1​:ρ<0
 
F.
H Subscript 0​:β Subscript 1≥0
H Subscript 1​:β Subscript 1<0
Part 3
Compute the test statistic.
 
The test statistic is______enter your response here.
​(Round to two decimal places as​ needed.)
Determine the​ p-value.
The​ p-value is
enter your response here.
​(Round to three decimal places as​ needed.)
 
Reach a decision.
 
▼
 Reject
Do not reject
H Subscript 0. There is
▼
 insufficient
sufficient
evidence at the 0.05 level of significance to conclude that there is a significant linear relationship between calories and sugar.
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