Question

after a product recall, a company solicits feedback from a random sample of 100 customers regarding their opinion about the company since the recall. customers were asked, \do you approve, disapprove, or have no opinion about the company?\ the public relations department is concerned that the opinions may be equally distributed across those three options. they decide to carry out a test of significance. are the conditions for inference met?
no, the random condition is not met.
no, the 10% condition is not met.
no, the large counts condition is not met.
yes, all of the conditions for inference are met.

Explanation:

Step1: Check Random Condition

The problem states it's a random sample of 100 customers. So random condition is met.

Step2: Check 10% Condition

We assume the company has more than \(10\times100 = 1000\) customers (since it's a company that had a product recall). So 10% condition is met.

Step3: Check Large Counts Condition

If opinions are equally distributed, expected count for each category \(E=\frac{n}{k}\), where \(n = 100\) (sample size) and \(k=3\) (number of categories). So \(E=\frac{100}{3}\approx33.33\geq5\). Large Counts condition is met.

Answer:

Yes, all of the conditions for inference are met.