Question

[2] A research study was conducted to examine the impact of eating a high protein breakfast on adolescents' performance during a physical education physical fitness test. Half of the subjects received a high protein breakfast and half were given a low protein breakfast. All of the adolescents, both male and female, were given a fitness test with high scores representing better performance. Test scores are recorded below. Protein Male Gender Female a) Analyze the data and draw conclusions. (30 points) b) Plot table of means. Give your comments. (10 points) c) Give your recommendations for Male and Female. (15 points) d) Analyze the residuals. (15 points)

Answer 1

(a)

Source	SS	df	MS	F	p-value
Gender	45.00	1	45.000	20.00	.0004
Protein	20.00	1	20.000	8.89	.0088
Interaction	5.00	1	5.000	2.22	.1555
Error	36.00	16	2.250
Total	106.00	19

The hypothesis being tested is:

H0: There is no main effect of Gender

Ha: There is a main effect of Gender

The p-value is 0.0004.

Since the p-value (0.0004) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a main effect of Gender.

The hypothesis being tested is:

H0: There is no main effect of Protein

Ha: There is a main effect of Protein

The p-value is 0.0088.

Since the p-value (0.0088) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a main effect of Protein.

The hypothesis being tested is:

H0: There is no interaction effect

Ha: There is an interaction effect

The p-value is 0.1555.

Since the p-value (0.1555) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is an interaction effect.

(b) The plots are:

Interaction Plot by Factor 1 Cell Mean Male Female High *Low

Interaction Plot by Factor 2 Cell Mean Low High -- Male + Female

There is significant main factors effect.

(c)

	High	Low
Male	8.0	5.0
Female	4.0	3.0

Females should eat more protein diet.

(d) The residuals are:

Versus Fits (response is 03) . . . Residual . . Fitted Value

The residuals are not normally distributed.

	High	Low
Male	10	5	Male	High	10
	7	4	Male	High	7
	9	7	Male	High	9
	6	4	Male	High	6
	8	5	Male	High	8
Female	5	3	Female	High	5
	4	4	Female	High	4
	6	5	Female	High	6
	3	1	Female	High	3
	2	2	Female	High	2
			Male	Low	5
			Male	Low	4
			Male	Low	7
			Male	Low	4
			Male	Low	5
			Female	Low	3
			Female	Low	4
			Female	Low	5
			Female	Low	1
			Female	Low	2

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