Question

Which of the following is correct based on the data?

a. The amount of caffeine consumed has an effect on cycling endurance

b. The amount of caffeine consumed does not have an effect on cycling endurance

c. None of the answer choices is correct

How many treatments and block are used in the experiment?

a. 4 blocks and 9 treatments

b. 9 blocks and 4 treatments

c. None of the other answer choices is correct

What is the p-value calculated for the effect of caffeine on cycling endurance time?

a. .00359

b. .00000042

c. None of the other answer choices is correct

	0mg	5mg	9mg	13mg
C1	36.05	42.47	51.5	37.55
C2	52.47	85.15	65	59.3
C3	56.55	63.2	73.1	79.12
C4	45.2	52.1	64.4	58.33
C5	35.25	66.2	57.45	70.54
C6	66.38	73.25	76.49	69.47
C7	40.57	44.5	40.55	46.48
C8	57.15	57.17	66.47	66.35
C9	28.34	35.05	33.17	36.2
						The dataset contains cycling times of 9 cyclists on 4 different levels of caffeine. Develop your hypotheses and at .05 significance level conduct the appropriate statistical test to determine if different levels of caffeine have any effect on cycling endurance times. Build the ANOVA table. Make sure you account for the variation that might have contributed by the cyclists.

Answer 1

We input the two-way ANOVA data into MS Excel and then build an ANOVA table using the "Anova: Two-Factor Without Replication" option under Data > Data Analysis. The screenshot of the data and the output is given below. We use the output to answer our questions.



(1) Since the p-value corresponding to Columns (amount of caffeine) is less than 0.05, we reject null hypothesis of independence and conclude that - The amount of caffeine consumed has an effect on cycling endurance.

(2) Since there are 9 cyclists on 4 different levels, we can say that there are 9 blocks and 4 treatments.

(3) The p-value for the effect of caffeine on cycling endurance time = 0.00359.