Question

a manufacturer of large kitchen appliances keeps track of the costs of warranty claims. management suspects that 75% of all warranty claims are invalid, 20% cost the company less than $500, and 5% of them cost the company more than $500. to investigate this belief, a random sample of 80 warranty claims is selected from their vast records of past warranty claims. the management would like to know if the distribution of claim results differs from what they suspect. 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

A random sample of 80 warranty claims is selected. So, the random condition is met.

Step2: Check 10% Condition

Assume the company has a vast number of past warranty claims. If \(N\) (total number of claims) is large, and \(n = 80\), then \(n=80<0.1N\) (since \(N\) is vast). So, the 10% condition is met.

Step3: Check Large Counts Condition

For invalid claims: \(np_1=80\times0.75 = 60\)
For claims costing less than $500: \(np_2=80\times0.20=16\)
For claims costing more than $500: \(np_3=80\times0.05 = 4\)
Since \(np_3 = 4<5\), the large - counts condition (where \(np_i\geq5\) for all \(i\)) is not met.

Answer:

No, the Large Counts condition is not met.