A random sample of 100 HD projectors from manufacturer A had 15% being defective

Question

A random sample of 100 HD projectors from manufacturer A had 15% being defective. From manufacturer B, a random sample of 200 HD projectors showed 10% being defective. I claim that the population proportion of defective HD projectors for manufacturer A is greater than the population proportion for manufacturer B. Write down your statistical hypotheses, your test statistic formula, your test statistic value, and the p-value. Interpret the p-value. You may assume manufacturers A and B are independent.

Explanation / Answer

Test and CI for Two Proportions

Sample X N Sample p
1 15 100 0.150000
2 20 200 0.100000

Difference = p (1) - p (2)
Estimate for difference: 0.05
95% lower bound for difference: -0.0183159
Test for difference = 0 (vs > 0): Z = 1.20 P-Value = 0.114

Fisher's exact test: P-Value = 0.140

P-value >0.05 we do not reject the null hypotheis we conclude that there is no population proportion of defective HD projects for manufacturer A is greater that the B.

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