Question

Calculate ANOVAs for the following two problems. Show all your work.

First-born children tend to develop language skills faster than their younger siblings. One possible explanation is that they have undivided attention from their parents. If this is correct, then twins should show slower language development than single children, and triplets should be even slower. The following hypothetical data demonstrate potential measure of language skill from such a study. Do the data indicate significant differences?

Single Child: 8, 7, 10, 6, 9

Twin: 4, 6, 7, 4, 9

Triplet: 4, 4, 7, 2, 3

This study examined how long it took for mothers to get their children back home, when the children were 5 months, 20 months, and 35 months old.

5 months: 15, 10, 25, 15, 20, 18

20 months: 30, 15, 20, 25, 23, 20

35 months: 40, 35, 50, 43, 45, 40

Answer 1

Answer:-

Given That:-

Calculate ANOVAs for the following two problems. Show all your work. First-born children tend to develop language skills faster than their younger siblings. One possible explanation is that they have undivided attention from their parents. If this is correct, then twins should show slower language development than single children, and triplets should be even slower. The following hypothetical data demonstrate potential measure of language skill from such a study. Do the data indicate significant differences?

	Group 1	Group 2	Group 3
	8	4	4
	7	6	4
	10	7	7
	6	4	2
	9	9	3
Sum =	40	30	20
Average =	8	6	4
	330	198	94
Standard Deviation	1.581	2.121	1.871
SS =	10	18	14
n =	5	5	5

The total sample size is N = 15.

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 needto 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 tha sum of squares are computed, we can proceed with computing the mean sum of squares:

= 40/2

= 20

= 42/12

= 3.5

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

= 20/3.5

= 5.714.

Thank you for your supporting....please upvote my answer.....