Rates of Return Financial Energy Utilities 10.73 12.89 11.88 15.05 13.96 5.76 17.21 6.33 13.46 5.07 11.23 9.90 19.59 18.79 3.95 8.21 20.73 3.44 10.45 9.60 7.11 6.75 17.40 15.70 A stock analyst wondered whether the mean rate of return of financial, energy, and utility stocks differed over the past 5 years. He obtained a simple random sample of eight companies from each of the three sectors and obtained the 5-year rates of return shown in the accompanying table (in percent). Complete parts (a) through (d) below. Click the icon to view the data table. (a) State the null and alternative hypotheses. Choose the correct answer below. A. Ho: Pfinancial Henergy = Putilities and H: Pfinancial Henergy The table to the right contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has two categories. Use the table to complete parts (a) and (b) below. (a) Test the hypothesis that X and Y are independent at the = 0.01 level of significance. OA. Ho: The Y category and X category are independent. H: The Y category and X category are dependent. OB. Ho: x-Ex and y = Ey H: H #E, or Hy #Ey OC. Ho: The Y category and X category have equal proportions. H: The proportions are not equal. OD. Ho: The Y category and X category are dependent. H: The Y category and X category are independent. (b) Compute the value of the chi-square test statistic. x = (Round to three decimal places as needed.) What is the P-value? P-value= (Round to three decimal places as needed.) X 30 2 X3 43 55 (33.57)(45.46)(48.96) 18 22 15 (14.43) (19.54)(21.04) Observed Distribution of Colors Colored Candies in a bag Color Brown Yellow Red Blue Orange Green Frequency 60 63 56 59 83 63 Claimed Proportion 0.13 0.14 0.13 0.24 0.20 0.16 Compute the expected counts for each color. Color Frequency Expected Count Brown 60 Yellow 63 Red 56 Blue 59 Orange 83 Green 63 (Round to two decimal places as needed.) What is the test statistic? x = (Round to three decimal places as needed.) What is the P-value of the test? P-value= (Round to three decimal places as needed.) 8