A manufacturer receives parts from two suppliers.A simple random sample of 400 parts from Supplier 1 finds 20 defective.A simple random sample of 200 parts from Supplier 2 finds 20 defective.Let p₁ and p₂ be the proportion of all parts from Supplier 1 and Supplier 2,respectively,that are defective.Is the difference statistically significant at the 5% significance level? To determine this,test the hypotheses H₀: p₁ = p₂ versus H_a: p₁ $\neq$ p₂.

Question

Quizplus · Accepted Answer

We can use a two-sample z-test for proportions to test the hypothesis.

The sample proportions are: 
p1̂ = 20/400 = 0.05 
p2̂ = 20/200 = 0.1

The sample standard errors are: 
SE1 = sqrt(p1̂(1-p1̂)/n1) = sqrt(0.05(0.95)/400) = 0.015 
SE2 = sqrt(p2̂(1-p2̂)/n2) = sqrt(0.1(0.9)/200) = 0.03

The test statistic is: 
z = (p1̂ - p2̂) / sqrt(SE1^2 + SE2^2) = (0.05 - 0.1) / sqrt(0.015^2 + 0.03^2) = -2.77

Using a standard normal distribution table or calculator, the p-value is found to be approximately 0.0056. Since the p-value is less than 0.05, we reject the null hypothesis and conclude that the difference in proportions is statistically significant at the 5% level.

A Manufacturer Receives Parts from Two Suppliers ≠\neq= P2

A Manufacturer Receives Parts from Two Suppliers $\neq$ P₂