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

Sample a sample a Y = 5 n. = 250 * - 5 n22 300 20.025 = 0.0967 W state hypothesis : P = Pz. Ho: Hai P. & P. ( Two tailed Test ) LP's Test statistics :- For - test we Proportion statistics will . use 2= h ê - (P. - P:) 6 (1-8, ) , (i=0. nz 0.095-0.0967 0.025 80.975 0.0267 x 0.9733 950 3oo 22 - 0.125 test statistics our in Zrest - olge 211

Critical Value method :- or uy. a = o.ou Tailed for Tawo Non - Rejection Region 00g 0.02 5 -2.094 = Z Z28.054 - Rejection Rejection Region Regection Region - 8 Zec-2.054 Zi ; 2.054 balls Decision on Ho :- . in Non we. Fail As Zrest = -0.125 rejection region so To Reject to have conclusion 2 - At sufficient claum of proportion ut significance level awe evidence to support the two mand facturers that defectives are essentially their the same.