2. The chi-square test for goodness of fit No preference Aa Aa A developmental p

Question

2. The chi-square test for goodness of fit No preference Aa Aa A developmental psychologist is studying bonding between healthy newborn babies and immediate family members. He wants to know if mothers use smell to recognize their one-week-old infants. To investigate, he selects a random sample of mothers of one-week-old infants. Each mother is presented with a garment worn by her infant and two garments worn by unrelated babies. He asks each of the mothers to identify her infant's garment. The resulting data are summarized in the following table that shows the number of mothers who selected each of the three garments. Actual Unrelated Unrelated Baby Baby #1 Baby #2 22 10 The developmental psychologist wants to know if mothers select the garment of their own one-week-old infant more often than might occur by chance. He plans to use a chi-square test for goodness of fit to test his hypothesis. The null hypothesis, that the mothers have no preference for the different garments, can be represented by the following, where the values specify the proportion of the population of mothers who would orient toward each of the garments Actual Unrelated Unrelated Baby Baby #1 Baby #2 Fill in the following table with the expected frequencies if the null hypothesis is true: Actual Unrelated Unrelated Baby Baby #1 Baby #2

Explanation / Answer

test stat chi square =8.600

has 2 degree of freedom

critical value is 5.991

since the chi square stat is greater then the critical value, the psychologist reject the null hypothesis

the psychologist has sufficient evidence to conclude that..

observed Expected Chi square X Probability O E=total*p =(O-E)^2/E actual 1/3 22.000 13.33 5.63 unrelated 1 1/3 8.000 13.33 2.13 unrelated 2 1/3 10.000 13.33 0.83 1 40 40 8.6000

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