# Question

“Climbing out of debt, step by step,” an article in the April 29, 2005, USA Today, reported results of a survey of 260 members of the Financial Planning Association. Financial planners each reported what he or she considers to be the one most valuable step people can take to improve their financial lives.

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.

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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