Mal-Al's Color Distribution: Suppose the makers of MBiM candies give the following average percentages for the mix of colors in their bags of plain chocolate MStM's. Stated Distribution of Colors Brown Yellow Red Oran ge Green Blue Percent 30% 20% 20% 10% 10% 10% Now, you randomly select 200 MEN'S and get the counts given in the table below. You expected about 20 blues but only got 9. You suspect that the maker's claim is not true. Observed Counts by Color (:1 = 200) Brown Yellow Red Orange Green Blue Count ?1 32 49 16 23 9 The Test: Test Iwhether or not the color of HELP-1's candies ts the distribution stated by the makers {Mars Company). Conduct this test at the 0.01 signicance level. [a] what is the null hypothesis for this test in terms of the probabilities ofthe outcomes? Ho: pm. = 0.30. 9..."... = 0.20. p... = 0.20. new. = 0.10. 0......n = 0.10. and so... = 0.10. O Ho: At least one of the probabilities doesn't t the company's statement. 0 Ho: The probabilities are not all equal to ll. O HO: pbl'otwn = pyellow = pred = \"orange = pgreen = pblue = 11(6- [b] The table below is used to calculate the test statistic. Complete the missing cells. Round your answers to the same number of decimal places as other armies for that column. Candy Observed Assumed Expected __ .2 1' Color Frequency (of) Probability (pi) Frequency (EF) (0' EB l' 1 Brown I: 0.30 50 2.012 2 Yellow 32 |:| 40 1.600 3 Red 49 0,20 |:| 2.025 4 Orange 16 0.10 20 |:| 5 Green 23 0,10 20 0.450 5 Blue 9 0.10 20 6.050 {c) What is the value for the degrees of freedom? |:| [d] What is the clitical value of 12 ? Use the answer found in the 12 lble or round to 3 decimal places. {e} Ill'lrhat is the conclusion regarding the null hypothesis? 0 reject Ha @ fail to reject Ho