Question

There are two decks of cards, and they both have an unknown number of cards. Both decks have two colors, which are red and black. We draw n cards from each deck with replacement. Let p1 be the proportion of cards in deck 1 that are red, and p2 be the proportion of cards in deck 2 that are red. Suppose we are testing Ho : p1 - p2 = 0 ; Ha : p1 - p2 = -0:03 with $\alpha$ = 0:01. Find a sample size n (common sample size, and not necessarily minimal) such that

Answer 1

utery. There are too decks of cards, and .ltry both have,0 on unkvon nurmber of Carala cks have too Coo, lhch are red & black each deck corlh replacement. Both dlec The PYopor at are, red 乡deck I :26 = 0.9615 2 0.0340 Σ, x (0.9615) → deck that-thre red-26 26 12

2) For Proportion 20 N드 Al 0,o009 N= 912. P-82 C2) 23.33 lest Stastistc Cz) StAT critical value 군0.01-2- ro 2.33 Test-Statistic 〉 CYittel value 3.33 > 2.33 Reject the Notl trapothesis (Ho) 、PL 군 〉 3.331 P-value '.'From z-table P-vave gntfronce levet) Reject the N yCHo) T is sgnifiant that P B ave not Same.