Question

A coworker claims that Skittles candy contains equal quantities of each color (purple, green, orange, yellow, and red). In other words, 1/5 of all Skittles are purple, 1/5 of all Skittles are green, etc. You, an avid consumer of Skittles, disagree with her claim. Test your coworker's claim at the α=0.10α=0.10 level of significance, using the data shown below from a random sample of 200 Skittles.

Which would be correct hypotheses for this test?

H0:H0: Red Skittles are cherry flavored; H1:H1: Red Skittles are strawberry flavored

H0:H0:Skittles candy colors come in equal quantities; H1:H1:Skittles candy colors do not come in equal quantities

H0:H0:Taste the Rainbow; H1:H1:Do not Taste the Rainbow

H0:p1=p2H0:p1=p2; H1:p1≠p2H1:p1≠p2

Sample Skittles data:

Color	Count
Purple	38
Green	34
Orange	38
Yellow	39
Red	51

Test Statistic:



Give the P-value:



Which is the correct result:

Reject the Null Hypothesis

Do not Reject the Null Hypothesis

Which would be the appropriate conclusion?

There is not enough evidence to reject the claim that Skittles colors come in equal quantities.

There is not enough evidence to support the claim that Skittles colors come in equal quantities

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: H0: Skittles candy colors come in equal quantities.

Alternative hypothesis: H1: Skittles candy colors do not come in equal quantities.

Formulate an analysis plan. For this analysis, the significance level is 0.10. Using sample data, we will conduct a chi-square goodness of fit test of the null hypothesis.

Analyze sample data. Applying the chi-square goodness of fit test to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = k - 1 = 5 - 1
D.F = 4
(E_i) = n * p_i


X² = 4.15

where DF is the degrees of freedom, k is the number of levels of the categorical variable, n is the number of observations in the sample, E_i is the expected frequency count for level i, O_i is the observed frequency count for level i, and X² is the chi-square test statistic.

The P-value is the probability that a chi-square statistic having 4 degrees of freedom is more extreme than 4.15

We use the Chi-Square Distribution Calculator to find P(X² > 4.15) = 0.386

Interpret results. Since the P-value (0.386) is greater than the significance level (0.10), we have to accept the null hypothesis.

Do not Reject the Null Hypothesis.

There is not enough evidence to reject the claim that Skittles colors come in equal quantities.