Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
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Textbook Question
Chapter 5.1, Problem 10E
The authors of the paper “Flat-footedness Is Not a Disadvantage for Athletic Performance in Children Aged 11 to 15 Years” (Pediatrics [2009]: e386-e392) studied the relationship between y = Arch height and scores on a number of different motor ability tests for 218 children. They reported the following
- a. Interpret the value of the
correlation coefficient between average hopping height and arch height. What does the fact that the correlation coefficient is negative say about the relationship? Do higher arch heights tend to be paired with higher or lower average hopping heights? - b. The title of the paper suggests that having a small value for arch height (flat-footedness) is not a disadvantage when it comes to motor skills. Do the given correlation coefficients support this conclusion? Explain.
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find the critical value
Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using alpha equals 0.05.
Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of theseals?
Overhead Width
7.1
7.6
9.7
9.3
8.6
8.2
Weight
115
197
243
198
197
186
Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using
α=0.01.
Overhead width
overhead weight
7.1
111
7.6
164
9.8
250
9.2
192
8.8
205
8.2
183
Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals?
The linear correlation coefficient is r=?
(Round to three decimal places as needed.)
The linear correlation coefficient is r=?
(Round to three decimal places as needed.)
The critical values are r=?
(Round to three decimal places as needed. Use a comma to separate answers as needed.)
Because the absolute value of the linear correlation coefficient is
______ than the positive critical value, there _______ sufficient evidence to support the claim that there is a linear…
Chapter 5 Solutions
Introduction To Statistics And Data Analysis
Ch. 5.1 - For each of the scatterplots shown, answer the...Ch. 5.1 - For each of the following pairs of variables,...Ch. 5.1 - For each of the following pairs of variables,...Ch. 5.1 - For each of the following pairs of variables,...Ch. 5.1 - Is the following statement correct? Explain why or...Ch. 5.1 - Draw a scatterplot for which r = 1.Ch. 5.1 - Draw a scatterplot for which r = 1.Ch. 5.1 - Each year J.D. Power and Associates surveys new...Ch. 5.1 - The accompanying data are x = Cost (cents per...Ch. 5.1 - The authors of the paper Flat-footedness Is Not a...
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Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using
α=0.05.
Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals?
Overhead Width
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7.6
9.8
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186
Click here to view a table of critical values for the correlation coefficient.
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Construct a scatterplot. Choose the correct graph below.
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710100300width (cm)weight (kg)
A scatterplot has a horizontal scale labeled “width in centimeters” from 7 to 10 in increments of 0.5 and a vertical scale labeled “weight in kilograms” from 100 to 300 in increments of 20. Six plotted points follow the pattern of a line rising…
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Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using
α=0.01.
Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals?
arrow_forward
Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using alpha equals 0.01 .Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals?
a. Construct a scatterplot.
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c. The critical values are r equals
(Round to three decimal places as needed. Use a comma to separate answers as needed.)
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Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using
α=0.01.
Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals?
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7.1
7.7
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201
242
204
197
192
Construct a scatterplot. Choose the correct graph below.
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(Round to three decimal places as needed.)
The critical values are
r=enter your response here.
(Round to three decimal places as needed. Use a comma to separate answers as needed.)
arrow_forward
Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using
α=0.05.
Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals?
Overhead Width Weight7.1 1147.5 1559.8 2499.3 1978.8 2008.1 182
The linear correlation coefficient is r=
The critical values are r=
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The authors of this study report a Pearson correlation coefficient estimate of r = 0.23 with a p-value of <0.01. Interpret.
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(a) Compute a 90% CI for the true correlation coefficient ?. (Round your answers to four decimal places.)
,
(b) Test H0: ? = −0.5 versus Ha: ? < −0.5 at level 0.05. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
z
=
P-value
=
State the conclusion in the problem context.
Reject H0. There is no evidence that ? < −0.5. Reject H0. There is evidence that ? < −0.5. Fail to reject H0. There is evidence that ? < −0.5. Fail to reject H0. There is no evidence that ? < −0.5.
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Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using
α=0.01.
Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals?
Overhead Width
7.1
7.6
9.7
9.4
8.8
8.2
Weight
111
198
246
204
202
185
Construct a scatterplot. Choose the correct graph below.
(inserted as picture)
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r=__________
(Round to three decimal places as needed.)
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(Round to three decimal places as needed. Use a comma to separate answers as needed.)
Because the absolute value of the linear correlation coefficient is
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Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using alpha equals 0.01. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals?
a. Construct a scatterplot.
b. The linear correlation coefficient is r=
(Round to three decimal places as needed.)
c. The critical values are
r=
(Round to three decimal places as needed. Use a comma to separate answers as needed.)
arrow_forward
Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using
α=0.05.
Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals?
Overhead Width
7.1
7.6
9.6
9.2
8.7
8.2
Weight
113
173
242
192
200
188
PLOTS INSERTED AS PICTURE
The linear correlation coefficient is
r=________.
(Round to three decimal places as needed.)
The critical values are
r=________.
(Round to three decimal places as needed. Use a comma to separate answers as needed.)
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▼
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greater
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is
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Internet Users (Per 100) Award Winners (Per 10 Million)80.6 5.478.1 8.956.5 3.368.3 1.678.9 10.938.8 0.1
C
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Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using α=0.05. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals?
Overhead Width 7.1 7.7 9.8 9.2 8.7 8.3
Weight 112 204 245 194 198 187
1. Construct a scatterplot graph
2. The linear correlation coefficient r is
3. The critical values are r=
4. Because the absolute value of the linear correlation coefficient is_____than the positive critical value, there___sufficient evidence to support the claim that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals for a significance level of α=0.05.
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