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 t

Chi-square tests
asked 2020-10-20
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 x2 test?
Nuts A company says its premium mixture of nuts con- tains 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 weigh- ing 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.

Answers (1)

Step 1
The data represents the hypothesis made by the company based on weights of the nuts.
Goodness of fit:
Goodness of fit test is applied to check how well the sample data obtained fits the distribution of the selected population. It can also be viewed as whether the frequency distribution fits the given pattern. Most commonly used test to check the goodness of fit is the chi-square test.
There are two values involved. They are observed and the expected values. The observed value represents the frequency of particular category in the sample and the expected value is obtained from the given distribution.
Moreover, it summarizes the difference between the expected and observed values of the given data.
Properties of goodness of fit:
-For each category, there is only one data value.
-Degrees of freedom is one less than the number of categories.
-Right tailed test is applied.
-It follows chi-square distribution
-If the categories are interchanged, the value of test statistic does not change.
Reason for the chi-square goodness of fit test is not appropriate to this hypothesis:
Therefore by considering the definition and given information, it is observed that the weight of the nuts does not follow the comparing counts (which specifies each unit with counts), since it is not a categorical data, and it follows the choice of quantitative.
Thus it is not appropriate to us the chi-square goodness fit test for the company hypothesis.
Step 2
b.The chi-square statistic is applied only when the counting of all possible value in each unit and which is the possible way.
Since here the claim of the company is not appropriate to tell whether it is the percentage by number or by weight and even the count cannot be predicted and thus chi-square statistic cannot be used.
Thus in order to use chi-square for the weights of nuts then counting of the data should be appropriate.
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