Answered

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The UR Nuts Company sells Deluxe and Premium nut mixes, both of which contain only cashews, brazil nuts, almonds, and peanuts. The Premium nuts are much more expensive than the Deluxe nuts. A consumer group suspects that the two nut mixes are really the same. To find out, the group took separate random samples of 20 pounds of each nut mix and recorded the weights of each type of nut in the sample. Here are the data:

Type of mix
Type of nut Premium Deluxe
Cashew 6lb 5lb
Brazil nut 3lb 4lb
Almond 5lb 6lb
Peanut 6lb 5lb

Required:
Explain why we can't use a chi-square test to determine whether these two distributions differ significantly.

Sagot :

akiran007

Answer:

No the conditions for this test are not met, as 20% of the data has expected value less than 5. And 37.5% data is equal to 5.

Step-by-step explanation:

The conditions for the chi square test independence are

1) the sample is a random sample

2) the variable under study is categorical

3) all expected value of the number of sample observations are greater or equal to 5.

A)The observations must be independent

B) for 2 categories the expected values must be at least 5

C) for the 3 categories the expected values must be at least 1 and no more than 20% may be smaller than 5

The observations given have equal chances of occurrences or are dependent on each other.

The sample collected has 20 % of data having expected values less than 5.

And 37.5% data is equal to 5.

We cannot use a chi-square test to determine whether these two distributions differ significantly because the expected value for some cells is less than 5.

What are the requirements for chi square test of independence?

  • The variables under study must be categorical
  • Sample is random sample
  • The expected frequency count for each cell of the contingency table is at least 5.

For the considered case, the sample is not large enough.

Although the sample was taken randomly and values are categorical, expected values are sometimes less than 5 for some cells of the contingency table.

Learn more about chi square test of independence here:

https://brainly.com/question/16956499

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