Question

Students in a high school statistics class wanted to see if the distribution of the colors of a popular candy was different in the bags for different types of candies the company manufactures. The students purchased several large bags of regular candies, tropical-flavored candies, and sour-flavored candies. For each type of candy, the students took a random sample of 100 candies and recorded how many of each color (red, green, yellow, or blue) were in the sample. The students verified the conditions for inference and calculated a chi-square test statistic of 12.59 with a corresponding p-value of 0.05. Which of the following is the correct interpretation of the p-value in the context of the test?

A The hypothesis test has a significance level of a = 0.05.
B There is a 5 percent chance that the distribution of colors is different for the different types of candies.
C There is a 5 percent chance that the distribution of colors is the same for the different types of candies.
D Assuming that the distribution of colors for the different types of candies is the same, there is a 5 percent chance of finding a test statistic of 12.59 or larger.
E Assuming that the distribution of colors for the different types of candies is different, there is a 5 percent chance of finding a test statistic of 12.59 or larger.

Answer 1

Assuming that the distribution of colors for the different types of candies is the same, there is a 5 percent chance of finding a test statistic of 12.59 or larger.

Explanation:

The null hypothesis is that there is no difference in the distribution of colors. Under the assumption that the null hypothesis is true, a p-value of 0.05 means that there is a 5 percent probability of obtaining a test statistic value as extreme as, or more extreme than, 12.59.

Answer 2

C There is a 5 percent chance that the distribution of colors is the same for the different types of candies.

Explanation:

The null hypothesis ; H0 : there is no difference in distribution of color for the different types of candies

Alternative hypothesis ; H1 : there is difference in the distribution of color for the different types of candies

When the Pvalue is < or = α ; we reject the null;

Here, the Pvalue and α = 0.05 ; hence, we reject the null.

A Pvalue of 0.05 means that there is only a 5% chance that the null is correct. That is ; There is only a 5 percent chance that the distribution of colors is the same for the different types of candies