Question

Below are weights (in pounds) of three groups of athletes. Athlete Group 1 Athlete Group 2 Athlete Group 3 246.00 280.00 295.00 282.00 225.00 304.00 230.00 277.00 291.00 220.00 274.00 308.00 267.00 258.00 270.00 344.00 302.00 315.00 325.00 278.00 305.00 309.00 290.00 300.00 334.00 200.00 277.00 384.00 260.00 311.00 201.00 285.00 295.00 197.00 220.00 299.00 186.00 222.00 311.00 278.00 284.00 205.00 280.00 a) (20 Points) Construct the complete ANOVA table, with appropriate row titles and column titles. You can use your caleulator to produce the ANOVA table values of SSG and SSE. You do not need to calculate the SSG or SSE manually.

Answer 1

(a)

Source	SS	df	MS	F	p-value
Treatment	10,971.04	2	5,485.522	3.22	.0506
Error	68,181.93	40	1,704.548
Total	79,152.98	42

(b) The hypothesis being tested is:

H₀: µ₁ = µ₂ = µ₃

H_a: Not all means are equal

The p-value is 0.0506.

Since the p-value (0.0506) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we cannot conclude that the three groups of athletes can be considered to have the same mean weight.

(c) r² = 10,971.04/79,152.98 = 0.139

13.9% of the variation in the model is explained.