3. A developmental psychologist would like to deter mine whether infants display any color preferences. A stimulus consisting of four color patches (red, green. blue, and yellow} is projected onto the ceiling above a crib. Infants are placed in the crib, one at a time, and the psychologist records how much time each infant spends looking at each of the four colors. The color that receives the most attention during a IOU-second test period is identied as the preferred color for that infant. The preferred colors for a sample of 80 infants are shown in the following table: Red Green Blue Yellow II" STE P 1 State the hypotheses and select an alpha level The hypotheses can be stated as follows: H\": In the general population, there is no preference for any specic orientation. Thus, the four possible orientations are selected equally often, and the population distribution has the following proportions: Top Up Bottom Left Side Right Side (Correct) Up Up Up Expected frequencies are computed and may be . _ _ _ decimal values. Observed H I: In the general population, one or more of the orientations is preferred over frequencies are always the others. '11 l b . \" 0 e \"um en We Will use or = .05. STE P 2 Locate the critical region For this example the value for degrees of freedom is rif=C1=41=3 For df = 3 and or = .05. the table of critical values for chisquare indicates that the critical X2 has a value of 181. The critical region is sketched in Figure 1?.4. STE P 3 Calculate the chi-square statistic The calculation of chisquare is actually a two stage process. First, you must compute the expected frequencies from Ho and then calcu- late the value of the chisquare statistic. For this example. the null hypothesis species that one-quarter of the. population (p = 25%) will be in each of the. four categories. According to this hypothesis, we should expect one-quarter of the sample to be in each category. With TA B L E 17. 3 The observed frequencies and the expected frequencies for the chi-square test in Example 17.2. a sample of n. = 50 individuals: the expected frequency for each category is 1 j; = pn = 4(50) = 12.5 The observed frequencies and the expected frequencies are presented in Table 17.3. Top Up Bottom Left Right {Correct} Up Side Up Side Up Observed Frequencies Expected Frequencies