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3. The chi-square test for goodness of fit- No preference Aa Aa A developmental psychologist is studying bonding between healthy newborn bables and immediate family members. He wants to know if mothers use smell to recognize their one-week-old infants. To investigate, he selects a randonm sample of mothers of one-week-old infants. Each mother is presented with a garment worn by her infant and two garments wom by unrelated babies. He asks each of the mothers to identify her infants 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 8 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 speciy the proportion of the population of mothers who would orient toward each of the garments: ActualUnrelated Unrelated Baby Baby #1 Baby #2 но: Fill in the following table with the expected frequendies if the null hypothesis is true Actual Unrelated Unrelated
Actual Unrelated Baby Baby #1 Raby #3 Hoi Fillin the following table with the expected frequencies if the nul hypotheeis e: ActualUarelated Uarelated Baby Baby # Raby #2 The chi-square statistic is x2 The distribution of the chi-square statistic has degreets) of freedom Use the following Distributions tool to find the critical yalue Chi-Square Distribution Degrees of Freedom3 With a .05, the critical value is the critical yalue,the payhelegist Since the chi-square statistic x2 is hypothesis The psychologist conclude that some mothers use smell 88 eegnie el 9ne week-le ifa
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