In: Statistics and Probability
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 | 400 | 760 | 770 | 810 | 850 | 1015 | 1190 | 1240 | 1310 | 1400 | 1475 | 1480 | 1505 | 2200 |
y | 3.80 | 3.90 | 5.00 | 5.20 | 4.10 | 3.60 | 6.40 | 6.88 | 7.55 | 4.95 | 7.70 | 4.45 | 6.50 | 8.90 |
Sxx = 2,617,030.357, Syy = 36.8158, Sxy = 7469.654. 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.
H0: ρ = 0
Ha: ρ ≠ 0H0:
ρ = 0
Ha: ρ <
0 H0: ρ =
0
Ha: ρ > 0H0:
ρ ≠ 0
Ha: ρ = 0
Compute the value of the sample correlation coefficient,
r. Round your answer to four decimal places.
r =
Calculate the test statistic and determine the P-value.
(Round your test statistic to two decimal places and your
P-value to three decimal places.)
t | = | |
P-value | = |
State the conclusion in the problem context.
Reject H0. A positive correlation exists between maximum lactate level and muscular endurance.
Reject H0. A positive correlation does not exist between maximum lactate level and muscular endurance.
Fail to reject H0. A positive correlation exists between maximum lactate level and muscular endurance.
Fail to reject H0. 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.)
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