Question

First-born children tend to develop language skills faster than their younger siblings. One possible explanation for this phenomenon is that first-borns have undivided attention from their parents. If this explanation is correct, then it is also reasonable that twins should show slower language development than single children and that triplets should be even slower. Davis (1937) found exactly this result. The following hypothetical data demonstrate the relationship. The dependent variable is a measure of language skill at age 3 for each child.

Single
Child Twin Triplet
8 6 5
7 4 5
10 6 8
6 7 3
9 4 5
8 9 4
Use an ANOVA with α = .05 to determine whether there are any significant mean differences among the three groups of children.

Answer 1

Explanation:

Hello!

The variable of interest is

Y: speed of language development on children

Factor: number of siblings

Levels of factors:

Single birth

Twins

Triplets

The claim is that the more siblings the child has, the slower he develops language abilities.

The hypotheses for the ANOVA are:

H₀: μ₁= μ₂= μ₃

H₁: At least one of the population means is different.

α: 0.05

`F= (MS_(Treatments))/(MS_(Errors)) ~~F_{Df_(Treatments); Df_(Errors)}`

`F= (14.00)/(2.80)= 5`

p-value= 0.0217

Using the p-value approach the decision rule is

p-value ≤ α, reject the null hypothesis.

p-value > α, do not reject the null hypothesis.

The p-value is less than the significance level, the decision is to reject the null hypothesis.

At 5% level of significance you can conclude that there is significance differences between the population means of language development on children of single birth, twins and triplets.