Question

You get a large shipment of components from each of 2 different manufacturers. A sample of 250 items from the first manufacturer’s shipment yields 5 defectives, and a sample of 300 items from the second manufacturer’s shipment yields 8 defectives. The two manufacturers claim that their proportion defectives are essentially the same. Test this claim at a 4% significance level. (State the null and alternative hypotheses. Be sure to clearly state the “rejection region” for the test, and state your conclusion in words.)

Answer 1

Given that,

For First manufacturer : n1 = 250, x1 = 5 and

For second manufacturer : n2 = 300, x2 = 8 and

Pooled proportion is,

The null and alternative hypotheses are,

H0 : p1 = p2

Ha : p1 ≠ p2

This hypothesis test is a two-tailed test.

Test statistic is,

=> Test statistic = Z = -0.51

critical values at significance level of 0.04 are, Zcrit = ± 2.05

Rejection Region : z < -2.05 or z > 2.05

Since, test statistic = -0.51 > -2.05, we fail to reject the null hypothesis (H0).

Conclusion : There is not sufficient evidence to warrant rejection of the claim that their proportion defectives are essentially the same.