I need help with questions 1B,1C, 1E, 1F. Questions 1A and 1D are already given. Thank you so much!

(1a) GIVNEN INFORMATION Distributions Color (1d) GIVEN INFORMATION QUESTION HINTS: Test Probabilities Yellow Level Estim Prob Hypoth Prob Concepts: Categorical data and testing categorical probabilities Red Blue 0.26563 0.166666667 Brown 0.12500 0.166666667 Goal: 1) To use a sample of candies to test a known distribution and 2) to compare distributions Green 0.12500 0.166666667 based on two categorical variables. Orange Orange 0.28125 0.166666667 Red 0.04688 0.166666667 Question 1: Goodness of Fit Test Green Yellow 0.15625 0.166666667 Set-up: The manufacturer of M&M candies claims that the colors in their plain candies have the following distribution: Brown Test ChiSquare DF Prob>Chisg Table 1: Distribution of Plain M&M colors from the Manufacturer Blue Likelihood Ratio 16.5763 0.0054* Type Blue Brown Green Orange Red Yellow Total Pearson 15.6875 0.0078* Plain 24% 13% 16% 20% 13% 14% 100% Data collection: In order to test the manufacturer's claim for plain M&M's, you collect a Frequencies Method: Fix hypothesized values, rescale omitted random sample of M&M's and the results are shown in the table below. Note: Hypothesized probabilities did not sum to 1. Probabilities have been rescaled. Level Count Prob Table 2: Random sample of Plain M&Ms by color. Blue 17 0.26563 Brown 8 0.12500 Color Total Green 3 0.12500 (le) Conclusion: Use your output to determine if you should reject or fail to reject the null Orange 18 0.28125 hypothesis at an alpha level of 0.05? Explain your answer using the p-value from the output. Blue 17 Red 3 0.04688 Brown 8 Yellow 10 0.15625 Total 1.00000 (1f) What is your opinion of the manufacturer's claim? Green 8 64 Orange 18 N Missing 1 Red 3 6 Levels Yellow 10 (1b) You would like to determine if the colors in your sample match the distribution claimed by Grand Total =64 the manufacturer. You may conduct a chi-square goodness of fit test. State the null and alternative hypotheses for this test. Note: The null hypothesis should pecify the proportion for each color. (1c) Verify that the assumptions for conducting this type of inference have been met