A firm that is planning to market a new cleaning product surveyed 1268 users of the leading competitor’s product. Each person rated the product as fair, good, or excellent. In addition, each person stated whether they use the product rarely (1), occasionally (2), or frequently (3).

The firm is interested in determining whether the rating given to the product is independent of the frequency with which the product is used. The following MINITAB output presents the results of a chi-square test for independence.

a. How many individuals who rarely use the product rated it good?

b. What is the expected number of individuals who used the product occasionally and rated it excellent?

c. Which of the nine combinations was least frequently observed?

d. Which of the nine combinations has the smallest expected count?

e. What is the P-value?

f. Can you conclude at the α = 0.05 level that rating and frequency of use are not independent? Explain.

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Chi-Square Test: Fair, Good, Excellent Expected counts are printed below observed counts Chi-Square contributions are printed below expected counts Good Excellent Fair Total 1 97 136 92 325 79.97 141.23 103.81 3.627 0.193 1.343 2 128 234 155 517 127.21 224.66 165.13 0.005 0.388 0.621 3 87 181 158 426 104.82 185.12 136.06 3.030 0.091 3.536 Total 312 551 405 1268 Chi-Sq 12.835, DF = 4, P-Value = 0.012 ==