91Ó°ÊÓ

Nuts A company says its premium mixture of nuts contains \(10 \%\) Brazil nuts, \(20 \%\) cashews, \(20 \%\) almonds, and 10 \(\%\) hazelnuts, and the rest are peanuts. You buy a large can and separate the various kinds of nuts. Upon weighing them, you find there are 112 grams of Brazil nuts, 183 grams of cashews, 207 grams of almonds, 71 grams of hazelnuts, and 446 grams of peanuts. You wonder whether your mix is significantly different from what the company advertises. a) Explain why the chi-square goodness-of-fit test is not an appropriate way to find out. b) What might you do instead of weighing the nuts in order to use a \(x^{2}\) test?

Offspring of certain fruit flies may have yellow or ebony bodies and normal wings or short wings. Genetic theory predicts that these traits will appear in the ratio 9: 3: 3: 1 (9 yellow, normal: 3 yellow, short: 3 ebony, normal: I ebony, short). A researcher checks 100 such flies and finds the distribution of the traits to be 59,20 \(11,\) and \(10,\) respectively. a) Are the results this researcher observed consistent with the theoretical distribution predicted by the genetic model? b) If the researcher had examined 200 flies and counted exactly twice as many in each category \(-118,40,22,\) \(20-\) what conclusion would he have reached? c) Why is there a discrepancy between the two conclusions?