One study investigated what children think about people who share their money (McCrink, Bloom, \& Santos, 2010). In this study, sixteen 5-year-olds were shown two puppets: One had a large number of coins, and the other had a small number of coins. Next, the two puppets gave the child some of their coins: One puppet gave the child 3 of its 12 coins, and the other puppet gave 1 of its 4 coins; although the number of coins given by the two puppets differed, the percentage was the same (i.e., \(3 / 12=1 / 4=25 \%\) ). The child then selected the puppet he or she thought was nicer: The "rich" puppet that started with more and gave more or the "poor" puppet that started with less and ended with less. Each child was categorized into one of three groups based on which puppet was thought to be nicer: the rich puppet, the poor puppet, or unsure. The researchers hypothesized that, even though the percentages were the same, children will think a puppet who gives a greater number of coins is nicer than a puppet who gives fewer coins. The selections for the sixteen 5 -year olds in this sample are presented below; conduct the chi-square goodness-of-fit test (assume equal hypothesized proportions):

a. Create a frequency distribution table and bar chart of these data.

b. State the null and alternative hypotheses \(\left(\mathrm{H}_{0}\right.\) and \(\left.\mathrm{H}_{1}\right)\).

c. Make a decision about the null hypothesis.
1, Calculate the degrees of freedom \((d f)\).

2, Set alpha (a), identify the critical value, and state a decision rule.
3, Calculate a statistic: chi-square \(\left(X^{2}\right)\).
4, Make a decision whether to reject the null hypothesis.
5, Determine the level of significance.
6, Calculate a measure of effect size (Cramér's \(\varphi\) ).

d. Draw a conclusion from the analysis.

e. Relate the result of the analysis to the research hypothesis.

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Puppet Puppet Puppet Puppet Puppet Puppet Rich Unsure Rich Rich Rich Rich Rich Rich Unsure Rich Unsure Rich Rich Unsure Unsure Rich