Question

The following output analyzes the relationship between the age of the ultra runners and their run time (unit: hours) from the 5k ultra run. Use it to answer the questions that follow.

Summary Output Regression Statistics Multiple R 0.5482 R Square 0.3005 Adjusted R Square 0.2953 Standard Error 1.2652 Observations 135

Coefficients Standard Error t-Stat p-value Lower 95% Upper 95% Intercept 4.8582 0.4507 10.7332 9.6354E-20 3.9667 5.7497 Age 0.0573 0.0104 5.2444 1.0177E-06 0.0367 0.0779

Test whether the ultra runner's age is linearly related to the run times in 50k ultra marathon. Use the significance level α = 0.05.

STEP 1: Set up null and alternative hypotheses using statistical terms only.

H₀:  --- β0 β1 b0 b1  --- > ≠ < =
H_A:  --- b1 β1 β0 b0  --- < = > ≠

STEP 2: Check all conditions. Make sure to clearly state the name of the plot you are referencing and your answer is in context of the problem.

STEP 3: Find the test-statistic and p-value. If necessary, round your answers to four decimal places.

t =
p-value =

STEP 4: State the conclusion in statistical terms.

Reject the null hypothesis.Fail to reject the null hypothesis.    

State the conclusion in and problem context.

Answer 1

1)

H0:  --- β1 = 0
HA:  --- β1 ╪ 0

3) test stat =  5.2444

p value=0.000

1.0177E-06 or 0.0000

4)Reject the null hypothesis