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A bakery sells cakes, cookies, and pastries. They wonder if customers are equally likely to buy each product. They take a sample of 200 recent purchases and record what was purchased (they are willing to treat this as a random sample). Here are the results

Product Cakes Cookies Pastries
Observed purchases 65 68 67

They want to perform a x^2 goodness-of-fit test to determine if these results suggest that one type of product is more popular than the others. What is the expected count of cake purchases?

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Answer:

66.667 cakes

Step-by-step explanation:

The expected count or value in a goodness of fit test is the product of the expected percentage and the total count or sample size.

Since the samples are being treated as a random sample, hence, the expected percentage of each of cake, pastries and cookies is the same.

The expected count of cakes is :

100/3 % * sample size

33.3333% * 200

= 66.667 cakes

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