Suppose a consumer affairs representative for Mars Incorporated claims that M&M’s plain chocolate candies are mixed such that each large production batch has the following percentages of colored candies: 20% brown, 10%yellow, 10% red, 10% orange, 20% green, and 30% blue. To test this claim, a professor distributed small sample bags of M&M’s to students and had them count the number of candies of each color. The counts of the students were then pooled with the following results. At α=0.01, determine whether there is sufficient evidence to conclude that the percentages are different from what the representative claims. Candy Colors Brown Yellow Red Orange Green Blue Number of candies 198 108 111 123 201 257   Step 1 of 4 :   State the null and alternative hypotheses in terms of the expected proportion for each candy color. Please give numeric answer for part 1   H0: pbrown=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ pyellow=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ pred=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ porange=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯pgreen=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ pblue=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ Ha: There is a difference from the stated proportions. Step 2 of 4: Calculate expected values   Step 3 of 4 :   Compute the value of the test statistic. Round any intermediate calculations to at least six decimal places, and round your final answer to three decimal places. Step 4 of 4: draw conclusion and interpret the decision (is there enough evidence?)

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Suppose a consumer affairs representative for Mars Incorporated claims that M&M’s plain chocolate candies are mixed such that each large production batch has the following percentages of colored candies: 20% brown, 10%yellow, 10% red, 10% orange, 20% green, and 30% blue. To test this claim, a professor distributed small sample bags of M&M’s to students and had them count the number of candies of each color. The counts of the students were then pooled with the following results. At α=0.01, determine whether there is sufficient evidence to conclude that the percentages are different from what the representative claims.

Candy Colors
Brown Yellow Red Orange Green Blue
Number of candies 198 108 111 123 201 257
 
Step 1 of 4 :  
State the null and alternative hypotheses in terms of the expected proportion for each candy color. Please give numeric answer for part 1
 
H0: pbrown=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ pyellow=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ pred=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ porange=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯pgreen=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ pblue=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
Ha: There is a difference from the stated proportions.
Step 2 of 4: Calculate expected values
 
Step 3 of 4 :  
Compute the value of the test statistic. Round any intermediate calculations to at least six decimal places, and round your final answer to three decimal places.
Step 4 of 4: draw conclusion and interpret the decision (is there enough evidence?)
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