Question

Hello, I have been trying to answer this question for the last hour and I am still struggling could someone help me? The deadline is in 1hour!

Perform an analysis of variance on the following data set. Do this by answering the questions below.

Group 1	Group 2	Group 3
82	87	97
91	90	99
93	91	104
94	99	105
94	101	106
95	115	109
99	118	110
101	114
103	117
105	121
106	121
106	129
113
127

Link to spreadsheet.

1. What is SST?

2. What is the test statistic from ANOVA?

3. What is the p-value from ANOVA?

4. Consider the null hypothesis that there are no differences between the means of the three populations from which the three columns were sampled. Should this hypothesis be rejected at the 5% level?

Answer 1

The following table is obtained:

	Group 1	Group 2	Group 3
	82	87	97
	91	90	99
	93	91	104
	94	99	105
	94	101	106
	95	115	109
	99	118	110
	101	114
	103	117
	105	121
	106	121
	106	129
	113
	127
Sum =	1409	1303	730
Average =	100.643	108.583	104.286
	143357	143709	76268
St. Dev. =	10.924	14.222	4.821
SS =	1551.214	2224.917	139.429
n =	14	12	7

The total sample size is N = 33. Therefore, the total degrees of freedom are:

Also, the between-groups degrees of freedom are

, and the within-groups degrees of freedom are:

First, we need to compute the total sum of values and the grand mean. The following is obtained

Also, the sum of squared values is

Based on the above calculations, the total sum of squares is computed as follows

The within sum of squares is computed as shown in the calculation below:

The between sum of squares is computed directly as shown in the calculation below:

Now that sum of squares are computed, we can proceed with computing the mean sum of squares:

Finally, with having already calculated the mean sum of squares, the F-statistic is computed as follows:

Null and Alternative Hypotheses

Ha: At least one mean is not same.

Test Statistics

p-value = 0.2266

(3) Decision about the null hypothesis

As p = 0.2266 > 0.05, it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that not all 3 population means are equal, at the 0.05 significance level.