Question

A company says its premium mixture of nuts contains ​% Brazil​ nuts, ​% ​cashews, ​% ​almonds, and ​% ​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 grams of Brazil​ nuts, grams of​ cashews, grams of​ almonds, grams of​ hazelnuts, and grams of peanuts. You wonder whether your mix is significantly different from what the company advertises.

1) Explain why the chi-square goodness-of-fit test is not an appropriate way to find out.
A) The chi-square goodness-of-fit test can only be used on counts, weights are quantitative, not counts.
B) The chi-square goodness-of-fit test can only be used on quantitative variable, weights are counts, not quantitative variables.
C) The expected values are percentages, and the actual values are not. Therefore the ch-square goodness-of-fit test cannot be used.
D) The chi-square goodness-of-fit test cannot be use to test this kind of claim
2) What might you do instead of weighing the nuts in order to use a X2 test?
A) There is no way of performing a test without using weight.
B) Count the number of each kind of nut, assuming the company's percentages are based on counts rather than weights.
C) Find the volume of each kind of nut, assuming the company's percentages are based on volume.

Answer 1

A) The chi-square goodness-of-fit test can only be used on counts, weights are quantitative, not counts.

B) Count the number of each kind of nut, assuming the company's percentages are based on counts rather than weights.

Explanation:

The Test of Goodnes for fit is based on the property that the χ² test is applicable when the cell probabilities depend on unknown parameters, provided that the unknown parameters are replaced with their estimates and provided that the one degree of freedom is deducted from each parameter estimated.

1) So if the estimates ( counts) are missing the test is not applicable.

2) Percentages if treated as counts can be used for the χ² test.