The authors of a paper presented a correlation analysis to investigate the relationship between maximal lactate level x and muscular endurance y. The accompanying data was read from a plot in the paper. 390 740 780 790 860 1,035 1,190 1,240 1,310 1,390 1,465 1,490 1,515 2,190 y 3.90 4.10 5.00 5.30 4.10 3.60 6.20 6.78 7.65 5.05 7.90 4.35 6.50 9.00 Sxx = 2,626,273.214, Syy 37.2441, S7,371.232. A scatter plot shows a linear pattern. (a) Test to see whether there is a positive correlation between maximal lactate level and muscular endurance in the population from which this data was selected. (Use a = 0.05.) State the appropriate null and alternative hypotheses. O Ho: P = 0 H₂:p>O OHO: PO M O Ho: P-O H₂:p<0 O H₂: p=0 H₂: p=0 r= Compute the value of the sample correlation coefficient, r. (Round your answer to four decimal places.) Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.) t- P-value= State the conclusion in the problem context. O Reject Ho. A positive correlation does not exist between maximum lactate level and muscular endurance. O Fail to reject Ho. A positive correlation exists between maximum lactate level and muscular endurance. O Reject H.. A positive correlation exists between maximum lactate level and muscular endurance. O Fail to reject Ho. A positive correlation does not exist between maximum lactate level and muscular endurance. (b) If a regression analysis were to be carried out to predict endurance from lactate level, what proportion of observed variation in endurance could be attributed to the approximate linear relationship? Answer the question without doing any regression calculations. (Round your answer to four decimal places.) If a regression analysis were to be carried out to predict lactate level from endurance, what proportion observed variation in endurance could be attributed to the approximate linear relationship? Answer the question without doing any regression calculations. (Round your answer to four decimal places.)
The authors of a paper presented a correlation analysis to investigate the relationship between maximal lactate level x and muscular endurance y. The accompanying data was read from a plot in the paper. 390 740 780 790 860 1,035 1,190 1,240 1,310 1,390 1,465 1,490 1,515 2,190 y 3.90 4.10 5.00 5.30 4.10 3.60 6.20 6.78 7.65 5.05 7.90 4.35 6.50 9.00 Sxx = 2,626,273.214, Syy 37.2441, S7,371.232. A scatter plot shows a linear pattern. (a) Test to see whether there is a positive correlation between maximal lactate level and muscular endurance in the population from which this data was selected. (Use a = 0.05.) State the appropriate null and alternative hypotheses. O Ho: P = 0 H₂:p>O OHO: PO M O Ho: P-O H₂:p<0 O H₂: p=0 H₂: p=0 r= Compute the value of the sample correlation coefficient, r. (Round your answer to four decimal places.) Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.) t- P-value= State the conclusion in the problem context. O Reject Ho. A positive correlation does not exist between maximum lactate level and muscular endurance. O Fail to reject Ho. A positive correlation exists between maximum lactate level and muscular endurance. O Reject H.. A positive correlation exists between maximum lactate level and muscular endurance. O Fail to reject Ho. A positive correlation does not exist between maximum lactate level and muscular endurance. (b) If a regression analysis were to be carried out to predict endurance from lactate level, what proportion of observed variation in endurance could be attributed to the approximate linear relationship? Answer the question without doing any regression calculations. (Round your answer to four decimal places.) If a regression analysis were to be carried out to predict lactate level from endurance, what proportion observed variation in endurance could be attributed to the approximate linear relationship? Answer the question without doing any regression calculations. (Round your answer to four decimal places.)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 8E
Related questions
Question
Q9
Transcribed Image Text:The authors of a paper presented a correlation analysis to investigate the relationship between maximal lactate level x and muscular endurance y. The accompanying data was read from a plot in the paper.
x 390
740
OH: P = 0
780
y 3.90 4.10 5.00 5.30 4.10 3.60 6.20
H₂: p=0
OH₂: P = 0
H₂: P<0
O Ho: P = 0
H₂: P = 0
r =
790
860 1,035 1,190 1,240 1,310 1,390 1,465 1,490 1,515
6.78
Sxx = 2,626,273.214, Syy = 37.2441, Sxy= 7,371.232. A scatter plot shows a linear pattern.
(a) Test to see whether there is a positive correlation between maximal lactate level and muscular endurance in the population from which this data was selected. (Use α = 0.05.)
State the appropriate null and alternative hypotheses.
O Ho: P = 0
H₂:p> 0
7.65
5.05 7.90 4.35
6.50
Compute the value of the sample correlation coefficient, r. (Round your answer to four decimal places.)
2,190
9.00
Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.)
t =
P-value =
State the conclusion in the problem context.
O Reject Ho. A positive correlation does not exist between maximum lactate level and muscular endurance.
O Fail to reject Ho. A positive correlation exists between maximum lactate level and muscular endurance.
O Reject Ho. A positive correlation exists between maximum lactate level and muscular endurance.
O Fail to reject Ho. A positive correlation does not exist between maximum lactate level and muscular endurance.
(b) If a regression analysis were to be carried out to predict endurance from lactate level, what proportion of observed variation in endurance could be attributed to the approximate linear relationship? Answer the question without doing any regression calculations. (Round your answer to four decimal places.)
If a regression analysis were to be carried out to predict lactate level from endurance, what proportion of observed variation in endurance could be attributed to the approximate linear relationship? Answer the question without doing any regression calculations. (Round your answer to four decimal places.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning