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Eunice, a developmental psychologist, is investigating how styles of play diffe...

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Eunice, a developmental psychologist, is investigating how styles of play differ for 3-year-old boys and girls. In her experiment, she brings each child into a room with three play stations set up. One station has a set of blocks, one has a collection of toy cars, and the third features a dollhouse. The child is told that he or she can play at one and only one station. His or her choice is recorded, the child is allowed to play for 15 minutes, and then he or she leaves and the next child is brought in. The children’s choices are below. Based on these data, is it possible to conclude that there is an association between gender and chosen toy? Test at a level of significance of 0.05.

Q13 toy

a. State the null and alternative hypotheses. [2 marks]

b. What is the formula for the test statistic? [1 mark]

c. Check conditions and find the value of the test statistic. [4 marks]

d. Find the p-value. [2 marks]

e. Make a decision and state your conclusion in the context of the question. [2 marks]

f. Find the marginal distribution of gender. [1 mark]

g. Find the conditional distribution of toys for each gender. [2 marks]

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