Question 1171004: If the p-value for the Levene’s Test in an Oneway ANOVA equals .069, which of the following is the correct test to use for the MAIN hypothesis test?
a. Bonferroni
b. Games-Howell
c. Welch
d. ANOVA - F
I got B am I correct??
7. Which of the following is an appropriate notation for the Alternative/Research Hypothesis in an Oneway ANOVA?
a. H0 : µ1 = µ2
b. H0 : µD = 0
c. H0 : µ1 = µ2 = µ3
d. H1 : µ1 ≠ µ2 ≠ µ3
e. H1 : Not all means are equal
f. Both C & E
I got E am I correct??
8. Researchers are examining whether or not there are significant differences in sentence lengths (measured in months) across three types of offenders (property, violent, and drug offenders). To do this, they conduct a Single Factor Between Subjects ANOVA. One of the researchers notices that the p-value for the Levene’s test equals .032. Based on this information, can the researchers conclude there is a significant difference in sentence length across different offenses types?
a. Yes
b. No
I got A am Icorrect??
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Let's break down each question:
**1. Levene's Test and ANOVA Choice:**
* **Levene's Test** checks for the homogeneity of variances (whether the variances of the groups are equal).
* A p-value of 0.069 indicates that the variances are not significantly different at the 0.05 level (since 0.069 > 0.05). Therefore, you do not need to use a test that deals with unequal variances.
* **ANOVA - F** is the standard test when variances are assumed to be equal.
* **Welch's test** is used when variances are unequal.
* **Games-Howell** is a post-hoc test used when variances are unequal.
* **Bonferroni** is a post-hoc test used when variances are assumed to be equal.
**Therefore, the correct answer is d. ANOVA - F. You are incorrect.**
**2. Alternative Hypothesis in Oneway ANOVA:**
* **H0 (Null Hypothesis):** All group means are equal (e.g., µ1 = µ2 = µ3).
* **H1 (Alternative Hypothesis):** At least one group mean is different.
* Option e. "H1 : Not all means are equal" accurately reflects this.
* Option d. "H1 : µ1 ≠ µ2 ≠ µ3" is too restrictive. It implies that *every* mean is different from *every* other mean, which isn't necessary for the alternative hypothesis to be true.
**Therefore, the correct answer is e. You are correct.**
**3. Levene's Test and ANOVA Conclusion:**
* A p-value of 0.032 for Levene's Test indicates that the variances are significantly different at the 0.05 level (since 0.032 < 0.05).
* This violates the assumption of homogeneity of variances required for a standard ANOVA.
* If the assumption of homogeneity of variance is violated, then the researchers should not trust the results of the standard anova F test.
* Therefore, the researchers cannot conclude that there is a significant difference in sentence length across different offense types using the standard anova F test.
**Therefore, the correct answer is b. No. You are incorrect.**
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