USE EXCEL TO SHOW ALL YOUR WORK AND USE ALPHA 0.05 FOR ANY HYPOTHESIS TESTING Co

Question

USE EXCEL TO SHOW ALL YOUR WORK AND USE ALPHA 0.05 FOR ANY HYPOTHESIS TESTING

Company A launched a new process for producing silicon chips that has averaging 2.5% defective items (given this is normal for silicon chip products, the customer will accept the shipment if the defective ratio is at 3% or less). Here is the sampling plan their customer use to make the decision of accept/reject the shipment:

“For every 10,000 chips, 300 random samples will be selected and inspected, if there are more than 8 defective items in the 300 sample, the lot will be rejected.”

Questions 1 – what is the probability that a 10000 pieces shipment will be rejected by their customer?

Question 2 - The goal for Company A is to make sure more than 90% of their shipment will be accepted by their customer. In order to achieve the goal, Company A wants their customer to reduce the sample size from 300 samples. What sample size should Company A suggest to their customer? Show the analysis outcome to support your suggestion.

Explanation / Answer

Solution:-

1) The probability that a 10000 pieces shipment will be rejected by their customer is P(x > 8) = 0.33715.

p = 2.5/100 = 0.025

n = 300, x = 8

By applying binomial distribution:-

P(x, n, p) = nCx *px* (1 - p)(n - x)

P(x > 8) = 0.33715

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