The following data are from a completely randomized design. In the following calculations, use ? = 0.05. Treatment 1 Treatment 2 Treatment 3 62 82 68 46 71 54 53 88 61 39 63 45 xj 50 76 57 sj2 96.67 124.67 96.67
The following data are from a completely randomized design. In the following calculations, use
? = 0.05.
| Treatment 1 |
Treatment 2 |
Treatment 3 |
||
|---|---|---|---|---|
| 62 | 82 | 68 | ||
| 46 | 71 | 54 | ||
| 53 | 88 | 61 | ||
| 39 | 63 | 45 | ||
|
xj |
50 | 76 | 57 | |
|
sj2 |
96.67 | 124.67 | 96.67 |
a) Use analysis of variance to test for a significant difference among the means of the three treatments. State the null and alternative hypotheses:
A) H0: ?1 = ?2 = ?3
Ha: ?1 ≠ ?2 ≠ ?3
B) H0: Not all the population means are equal.
Ha: ?1 = ?2 = ?3
C) H0: ?1 = ?2 = ?3
Ha: Not all the population means are equal.
D)H0: ?1 ≠ ?2 ≠ ?3
Ha: ?1 = ?2 = ?3
E) H0: At least two of the population means are equal.
Ha: At least two of the population means are different.
Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value =
State your conclusion.
A) Do not reject H0. There is not sufficient evidence to conclude that the means of the three treatments are not equal.
B) Reject H0. There is not sufficient evidence to conclude that the means of the three treatments are not equal.
C) Do not reject H0. There is sufficient evidence to conclude that the means of the three treatments are not equal.
D)Reject H0. There is sufficient evidence to conclude that the means of the three treatments are not equal.
(b) Use Fisher's LSD procedure to determine which means are different. Find the value of LSD. (Round your answer to two decimal places.) LSD =
Find the pairwise absolute difference between sample means for each pair of treatments.
{x1 − x2} =
{x1 − x3}==
{x2 − x3}=
Which treatment means differ significantly? (Select all that apply.)
A) There is a significant difference between the means for treatments 1 and 2.
B) There is a significant difference between the means for treatments 1 and 3.
C) There is a significant difference between the means for treatments 2 and 3.
D) There are no significant differences
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