11.24 To demonstrate/explore the effect increased sample size has on the calculated chi-square value, let’s consider the Skittles candies in Exercise 11.23 and sample some larger bags of the candy.

a. Suppose we purchase a 16-oz bag of Skittles, count the colors, and observe exactly the same proportion of colors as found in Exercise 11.23:
Red Orange Yellow Green Purple 72 84 92 68 108 Calculate the value of chi-square for these data.
How is the new chi-square value related to the one found in Exercise 11.23? What effect does this new value have on the test results? Explain.

b. To continue this demonstration/exploration, suppose we purchase a 48-oz bag, count the colors, and observe exactly the same proportion of colors as found in Exercise 11.23 and part b of this exercise.
Red Orange Yellow Green Purple 216 252 276 204 324 Calculate the value of chi-square for these data.
How is the new chi-square value related to the one found in Exercise 11.23? Explain.

c. What effect does the size of the sample have on the calculated chi-square value when the proportion of observed frequencies stays the same as the sample size increases?

d. Explain in what way this indicates that if a large enough sample is taken, the hypothesis test will eventually result in a rejection.