in each case, determine whether the sample sizes are large enough to conclude th
ID: 3045269 • Letter: I
Question
in each case, determine whether the sample sizes are large enough to conclude that the sampling distribution of (p-2) is approximately normal. Complete parts a through e a. Determine if n, and n2 are both large enough n1 = 12, n2 = 14, p1 =0.44, p2 = 0.56 O No Yes b. Determine if ny and n2 are both large enough n, = 1 1. nz" 14, p1 = 0.93, p2-o85 O No Yes c. Determine if n1 and n2 are both large enough. n, = 30, n2 = 30, p1 = 0.72. P2-0.73 O No Yes d. Determine if n, and n2 are both large enough. n« 102, n' 249, p1 = 0.94, p' 0.95 O No e. Determine if n, and n2 are both large enough 128, n2 196. P10.07, P2 0.11 O Yes O NoExplanation / Answer
The normality conditions are met if n1*p1, n1(1-p1), n2p2 and n2(1-p2) are all greater than or equal to 10.
(a) n1 = 12, p1 = 0.44. n1*p1 = 12*0.44 = 5.28 which is less than 10. Hence No.
(b) n1 = 11, p1 = 0.93. n1*p1 = 11*0.93 = 10.23 and n1(1-p1) = 11*0.07 = 0.77, which is less than 10. Hence No.
(c) n1 = 30, p1 = 0.72. n1*p1 = 30*0.72 = 21.6 and n1(1-p1) = 30*0.28 = 8.4, which is less than 10. Hence No.
(d) n1 = 102, p1 = 0.94. n1*p1 = 102*0.94 = 95.88 and n1(1-p1) = 102*0.06 = 6.12, which is less than 10. Hence No.
(e) n1 = 128, p1 = 0.07. n1*p1 = 128*0.07 = 8.26, which is less than 10. Hence No.
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