(ch prob set Q2-5) Please answer all questions in the images. Note: for 4A, answer selections are "less than" or "greater than". For 4B, selections are: "reject" or "doesnt reject" and for 4C, selections are: "cannot" or "can". Please indicate which selections are correct in addition to completing the comuputations required for the images below.
restaurant manager wants to know if one of the three specials on the menu (baked fish, roast beef, or chicken salad) is more popular than the bthere. He selects a random sample of special orders and counts the number of orders in each category. The results are compiled in the following table. Fish Beef Chicken 48 46 53 Select the appropriate null hypothesis for this experiment. O One meal is more popular than the other two. O Customers prefer the baked fish to the roast beef. O There is no difference in popularity among the three meals. O One meal is less popular than the other two. Complete the following table of expected frequencies. Fish Beef Chicken The chi-square statistic for these data is y =With o = 0.05, the critical value is Since the chi-square statistic y? is A the critical value, the psychologist the null hypothesis. The psychologist conclude that some one-week-old infants use smell to recognize their fathers.2. Introduction to nonparametric tests Which of the following statements are true? Check all that apply. Nonparametric tests have no required assumptions. Parametric tests usually require more assumptions about the underlying population distribution of the data on which they are used than nonparametric tests. Nonparametric tests require the use of nominal or ordinal data.A developmental psychologist is studying bonding between healthy newborn babies and immediate family members. He wants to know if one-week-old infants use smell to recognize their fathers. To investigate, he selects a random sample of one-week-old infants. Each infant is presented with a garment worn by his or her father and two garments worn by unrelated men. The psychologist observes which garment each of the infants orients toward. The resulting data are summarized in the following table that shows the number of infants who oriented toward each of the three garments. Actual Father Unrelated Man #1 Unrelated Man #2 28 15 19 The developmental psychologist wants to know if one-week-old infants orient toward the garment of their own father 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 one-week-old infants have no preference for the different garments, can be represented by the following, where the values specify the proportion of the population of one-week-old infants who would orient toward each of the garments: Actual Father Unrelated Man #1 Unrelated Man #2 Ho: Fill in the following table with the expected frequencies if the null hypothesis is true: Actual Father Unrelated Man #1 Unrelated Man #2 The chi-square statistic is x' = The distribution of the chi-square statistic hes degree(s) of freedom.With the level of significance o = 0.01, the critical value is Because the chi-square statistic x? is the critical value, you the null hypothesis. Therefore, you Cconclude that the proportions of welfare recipients in the five household-size categories differ from the corresponding proportions for all US households.Suppose you are reading a study conducted in the year 2000 about welfare recipients in the United States. The authors report the following frequency data on the household size of the 1,844 welfare recipients in their random sample: Observed Frequencies Household Size 5-or-more-person 4-person 3-person 2-person 1-person 203 277 301 550 513 You wonder if welfare recipients tend to live in different-sized households than the US population at large. You obtain the following data from the 2000 census: Percent Distribution of US Households by Size Household Size 5-or-more-person 4-person 3-person 2-person 1-person 10.83% 14.20% 16.53% 32.63% 25.81% Source: Hobbs F., & Stoops, N. (2002). Census 2000 special reports: Demographic trends in the 20th century. US Census Bureau.] You use a chi-square test for goodness of fit to see how well the sample of welfare recipients fits the census data. What is the most appropriate null hypothesis? O The distribution of household sizes among welfare recipients is equal across the five household-size categories. O The distribution of household sizes among welfare recipients is different from that provided by the census data. O The distribution of household sizes among welfare recipients is the same as that provided by the census data. O The distribution of household sizes among welfare recipients is not equal across the five household-size categories. Fill in the missing values in the following table indicating the expected frequencies in each category for a sample size of 1,844, if the null hypothesis is true: Expected Frequencies Household Size 5-or-more-person 4-person 3-person 2-person 1-person 304.81 601.70 475.94 The chi-square statistic has been calculated for you: x" = 8.31. The distribution of the chi-square statistic has _ d degrees of freedom
