Please show full working out with english Thank You 2 A 1pou

Please show full working out with english. Thank You.

(2) A 1-pound bag of candy-coated chocolate-covered peanuts contained 224 pieces of candy, each colored brown, orange, green, or yellow. Test the null hypothesis that the machine filling these bags treats the four colors of candy equally likely; that is, test

The observed values were 42 brown, 64 orange, 53 green, and 65 yellow candies. You may select the significance level or give an approximate p-value.

Solution

Set up null and alternate as

H0: all means are equal

Ha: all means are not equal

Chi square = 4.15

df = 9

p =0.9013

The P-Value is 0.901265. The result is not significant at p < 0.05.

Hence accept null hypothesis that all means are equal

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H0:
All candies are equally likely

Ha: Atleast two candidates have difference preferences

Let us prepare chi square table with observed and expected

The P-Value is 0.100061. The result is not significant at p < 0.05.

Hence accept null hypothesis that all probabilities are equal.