Question

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 suppliers 1 and 2, respectively, that are defective.

Part A) What is the estimate for the difference in proportions, p₁ – p₂?

Part B) Is this difference statistically significant at the 5% significance level? To determine this, test the hypotheses H₀: p₁ = p₂ versus H_a: p₁ ≠ p₂

Answer 1

a)

p1cap = X1/N1 = 20/400 = 0.05
p1cap = X2/N2 = 20/200 = 0.1

p1-p2 = 0.05 - 0.1 = 0.05

b)

pcap = (X1 + X2)/(N1 + N2) = (20+20)/(400+200) = 0.0667

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 ≠ p2

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.05-0.1)/sqrt(0.0667*(1-0.0667)*(1/400 + 1/200))
z = -2.31

P-value Approach
P-value = 0.0209
As P-value < 0.05, reject the null hypothesis.