Question

For each exercise, assume that all variables are normally distributed, that the samples are independent, and that the population variances are equal. Also, for each exercise, perform the following steps: 1. State the hypotheses and identify the claim; 2. Find the critical value; 3. Compute the test value; 4. Make the decision to reject or not reject the null hypothesis; 5. Summarize the result.

Answer 1

Hypothesis:

H0: μ1 = μ2 = μ3

Ha: Not all the means are same

Critical value:

alpha = 0.05, df1 = 2 and df2 = 10

Fc = 4.1028 (Use F table)

Test:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Eastern third	5	177	35.4	351.8
Middle third	4	275	68.75	338.25
Western third	4	177	44.25	277.5833333
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	2570.376923	2	1285.188462	3.948715585	0.054456095	4.102821015
Within Groups	3254.7	10	325.47
Total	5825.076923	12

F stat = 3.9487

Decision:

Fstat = 3.9487 < F critical = 4.1082, Do not reject H0

Conclusion:

There is not enough evidence to warrant rejection of claim that the mean number of farms is the same across these three geographic divisions at 5% significance level