Question

Suppose a candy company representative daims that colored candies are mixed such that each large production batch has precisely the following proportions: 10% brown 20 yellow. 20% red, 10% orange, 20 % green, and 20 % blue. The colors present in a sample of 459 candies was recorded. Is the representative's claim about the expected proportions of each color refuted by the data? red green blue Color Number of Candies brown yellow 90 55 orange 44 159 67 44 Copy Dots Step 4 of 10: Find the expected value for the number of chocolate candies colored brown. Round your answer to two decimal places

Answer 1

Color	Brown	Yellow	Red	Orange	Green	Blue
Observed Candies	90	55	159	44	67	44
Expected Candies	459*10/100 =45.9	459*20/100 =91.8	459*20/100 =91.8	459*10/100 =45.9	459*20/100 =91.8	459*20/100 =91.8

Expected number of clocolate candies coloured brown = 45.90

Here, we perform the chi square goodness of fit test.

H₀: The representative's claim is not refuted by the data

H₁ : The representative's claim is refuted by the data

The chi square test statistic is given by,

1* = [ (0; – E:)! E;

Where is the observed value

O

and, is the expected value

E

- 42.3706 + 14.7521 + 49.1922 +0.0786 +6.6998 + 24.8893

  

= 137.983

The critical value for $\alpha = 0.05$ is given by,

$\chi_{\alpha,n-1}^2=\chi_{0.05,6-1}^2=\chi_{0.05,5}^2=11.070$

Here, since

$\chi_{obs}^2>\chi_{\alpha,n-1}^2$

We reject the null hypothesis at $\alpha = 0.05$ level of significance.

So, we have enough evidence to conclude that representative's claim about the expected proportions of each color is refuted by the data.

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