CHI-SQUARE TEST OF INDEPENDENCE x^2 = sigma [(f_o - f_e)^2/f_e] f_e = column tot

Question

CHI-SQUARE TEST OF INDEPENDENCE x^2 = sigma [(f_o - f_e)^2/f_e] f_e = column total x row total/n A researcher wanted to know if younger children (ages 6-9) are different from older children (ages 10-13) in whether they would prefer to play a game by themselves or with other children. She has 20 younger children and 20 older children come to the lab, and gives them a choice to play a game by themselves (alone) or with other children. The data are below. Conduct the appropriate test to determine if play choice (alone or with others) depends on a child's age. Set alpha at .05. H_o: ________ H_a: ________ Null Hypothesis: Retain Reject Significant difference? Yes No

Explanation / Answer

Using Minitab:

Tabulated Statistics: C1, Worksheet columns

Rows: C1   Columns: Worksheet columns

                     Younger     older
                    children children All

Play alone                14         8   22
                          11        11

play with others           6        12   18
                           9         9

All                       20        20   40

Cell Contents:      Count
                    Expected count

Pearson Chi-Square = 3.636, DF = 1, P-Value = 0.057
Likelihood Ratio Chi-Square = 3.696, DF = 1, P-Value = 0.055

H0: Younger children and older children are same.

H1: Younger children different than older children

P-value 0.055> 0.05 so do not reject null hypothesis.

So there is no significance difference between them.

Hope this will be helpful. thanks

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