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 α=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.
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 α=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
Answer: 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.
Explanation: The p-value indicates the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value, assuming the null hypothesis (same distribution of colors) is true.
Sourav
