Question

i need help on this goodness of fit problem!

Chapter 131 Goodness of Fi problem A developmental psychologist is wondering whether there is amy difference i A stimulus consisting of four color patches (red, green, blue, and yellow) is projected onto the ceilimng above a crib. Infants are placed in the crib, one at a time, and the each infant spends looking at each of the four colors. The color that receives the most attention during a test period is identified as the preferred color for that infant. The preferred colors for a total of 60 infants are shown in the following table, distributed across the four color categones: in infants' color preferences psychologist records how much time Yellow 10 Red 20 Green 12 Blue 18 Should the psychologist conclude there is any difference in the proportion of infants who prefer each of the four colors? Carry out the five steps of hypothesis testing for a Chi-Square Goodness of Fit (use alpha of.05). DO SO IN THE SPACE PROVIDED BELOW So that you may check your work, you should obtain a Chi-Square ) value of appx. 4.54 for this problem.

Answer 1

Goodness of fit problem: Observed Expected Hypothesis testing steps Step 1 H_0: Infant's crib is fair. H_1: Each colors appearing is unfair. Step 2 rightarrow Chasing the level of significance (alpha) (alpha = 0.05) If the results of over test fall into region of alpha, that means we can reject null hypothesis i.e: we can reject H_0. And accept the H_1. \r\n Step 3 Critical value For finding this, we need to find chi^2 value for alpha = 0.05. And degrees of freedom = possible outcomes - 1 = 4 - 1 = 3. So, the Blue are chi^2 = 0.15/4 = 4.086 Step 4: Test satisfies chi^2 = sum [(0 - E0^2)/E] = 4.086 (test satisfies) Since, 0.15 is less than the critical value. Step 5 So, we can not reject the null hypothesis. \r\n That means our infant cribs are fair and there is not any difference in proportion.