Question

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	1035	1210	1260	1290	1410	1475	1480	1505	2200
y	3.80	4.10	4.80	5.30	3.90	3.40	6.40	6.88	7.55	4.95	7.70	4.45	6.70	8.90

S_xx = 2,614,773.214, S_yy = 38.2727, S_xy = 7544.396. 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
H_a: ρ ≠ 0 H₀: ρ ≠ 0
H_a: ρ = 0     H₀: ρ = 0
H_a: ρ > 0 H₀: ρ = 0
H_a: 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.

Fail to 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.     Reject H₀. A positive correlation does not exist between maximum lactate level and muscular endurance. Reject H₀. A positive correlation exists between maximum lactate level and muscular endurance.

Answer 1

State the appropriate null and alternative hypotheses.

H_a: ρ = 0     H₀: ρ = 0

test staistic	3.978248352
P value==TDIST(3.98,12,1)	0.00092

Reject H₀. A positive correlation exists between maximum lactate level and muscular endurance.

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