To demonstrate explore the effect increased sample size has on the
To demonstrate/explore the effect increased sample size has on the calculated chi-square value, let’s consider the Skittles candies in Exercise 11.16 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 11.16:
Calculate the value of chi-square for these data. How is the new chi-square value related to the one found in Exercise 11.16? 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 11.16 and part a of this exercise.
Calculate the value of chi-square for these data. How is the new chi-square value related to the one found in Exercise 11.16? 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.
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