12.18. A psychologist studying young children is interested in the development o

Question

12.18.  A psychologist studying young children is interested in the development of color preferences among preschool boys. The psychologist hypothesizes that the boys would prefer certain colors to others.  For the purpose of the study, only five primary colors are included: yellow, red, blue, green, and black.  A group of 50 preschool boys are brought to a room and are asked to select one ball from a box full of balls.  In the box there are 50 yellow balls, 50 red, 50 blue, 50 green, and 50 black.  The colors of the balls chosen by the boys are recorded and a chi square test is used to analyze the data and answer the psychologist's research question.  The obtained chi square value is 8.800 (c2obt= 8.800) and the appropriate critical value is c2crit (.05,4) = 9.488. Following are the colors chosen by the boys:

Color

No. of Times the Color Was Chosen

(ObservedFrequencies)

Yellow

6

Red

12

Blue

14

Green

4

Black

14

a.Which chi square test was used to analyze the data? Explain.

b.What are the expected frequencies?

c.What are the study’s conclusions? Explain.

Color

No. of Times the Color Was Chosen

(ObservedFrequencies)

Yellow

6

Red

12

Blue

14

Green

4

Black

14

Explanation / Answer

ahere as we are checking if distribution of colors is equal in the box or not ; hence we are supposed to check for distribution fit,

for above  chi square test used should be goodness of fit,

b)expected frequency =np=50*(1/5)=10

c)as test statistic is not higher than critical value we can not reject null hypothesis of equal proportion.

we do not have evidence at 0.05 level to conclude that boys have preference for a particular color.

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