Solutions

Problem Part Solution
1 - ANOVA is a test for equality of several means. It allows us to compare the means for several groups in one hypothesis test.
2 - a. An F-distribution is right skewed. A t-distribution is bell-shaped.
b. The values of F are never negative. The values of t can be positive or negative.
c. The P-value for the ANOVA test is always the area in the right tail in an F-distribution. We will never divide the area in the tail. The P-value for a t-test can be either the area under the right tail, the left tail, or both.
3 - hist
4 - Elderly Females: n = 11, mean = 0.528, Std. Dev. = 0.112
Young Females: n = 10, mean = 0.645, Std. Dev. = 0.099
Elderly Males: n = 8, mean = 0.654, Std. Dev. = 0.092
Young Males: n = 9, mean = 0.558, Std. Dev. = 0.145
5 - ANOVA
6 - Yes, the requirements are satisfied. The requirements that were checked were the following:
-The observations are normally distributed within each group. This was checked by creating Q-Q plots for each group. The sample sizes are small and this conclusion is subjective.
QQEF
QQYF
QQEM
QQYM
-The variances are equal. This was checked by noting that the largest variance is not more than four times the smallest variance.
7 - \(H_0: \text{All the means are equal}\)
\(H_a: \text{At least one of the means differs}\)
8 - F = 2.932
df = 3 and 34
9 - P-value = 0.047
10 - P-value = 0.047 < 0.05 = \(\alpha\)
reject the null hypothesis
11 - There is sufficient evidence to suggest that there is a difference in the mean protein requirements of the individuals in the four groups.
12 - Hist12
13 - Control: n = 7, mean = 0.453, Std. Dev. = 0.391
MON: n = 7, mean = 0.521, Std. Dev. = 0.325
SAFF: n = 7, mean = 3.363, Std. Dev. = 0.774
SAFF/MON: n = 7, mean = 5.151, Std. Dev. = 0.729
14 - No, not all of the requirements are satisfied. The requirements that were checked were the following:
-The observations are normally distributed within each group. This was checked by creating Q-Q plots for each group. The sample sizes are small and this conclusion is subjective.
QQCON
QQMON
QQSAFF
QQSAFFM
-The variances are not equal. This was checked by noting that the largest variance is more than four times the smallest variance.
15 - \(H_0: \text{All the means are equal}\)
\(H_a: \text{At least one of the means differs}\)
16 - F = 106.217
df = 3 and 24
17 - P-value = 0
18 - P-value = 0 < 0.05 = \(\alpha\)
reject the null hypothesis
19 - There is sufficient evidence to suggest that there is a difference in the mean CLA content in milk fat for at least one of the four diets.
20 - It would be worth figuring out which of the diets produced the highest CLA content and then possibly encouraging the use of that diet more than the others.