Question

Data on 10 randomly selected athletes was obtained concerning their cardiovascular fitness (measured by time to exhaustion running on a treadmill and performance in a 20-km ski race. Both variables were measured in minutes and a regression analysis was performed. Ski- 86-2.5*Treadmill Coefficients Estimate Std. Error (Intercept)860.88 Treadmill 2.51.055 Is there sufficient evidence to conclude that there is a linear relationship between cardiovascular fitness and ski race performance? Round your answers to three decimal places. (a). The test statistic is (b). Using your answer from part (a), the p-value is (c). At the 5% significance level, we reject the null hypothesis and conclude that there is v evidence to conclude that there is a linear relationship between cardiovascular fitness and ski race perrormance

Answer 1

To test a linear relation exists between cardiovascular fitness and ski race performance we have to test β₁

Null hypothesis H₀ : β₁ = 0

Alternative hypothesis H₁ : β₁ ≠ 0

1. Test statistics = regerssion coefficient / SE = b / SE(b)

t stat (Treadmill) = -2.5/1.055 = -2.370

2. P value = 2*P(T > t) = =T.DIST.2T(t, n-2)

P value = 2*P(T > 2.370) = T.DIST.2T(2.370, 8) = 0.045

3. Since P value = 0.045 < 0.05 so we reject null hypothesis.

At 5% significant level, we reject the null hypothesis and conclude that there is sufficient evidence to conclude that there is linear relationship between cardiovascular fitness and ski race performance.