Question

Consider a one-sided hypothesis test of the mean where a is known and N is large. Find the level for n that should be used in each of the following: Ho90, p, 100, a 25, a .05, B = .10 Ho=50, H, 30, o = 15, a = .01, B= .05 Ho 1.52, H, 30, o = .5, a = .05, B .10 Mol 1,100, ,1,000,a = 100, a = .10, B = .20 a. b. с. d.

Answer 1

Using the formula

n = [2* (Za/2 + 2)*o?]/(. -M1)

(A) set the following values in the formula

20.05/2 = 1.96 Z3 = 1.28 0 = 25 Ho = 90 M = 100

we get

sample size n =

= [2 *(1.96 + 1.28)2 * 251/(90 – 100) = 13122/100 = 131.22 = 131 (rounded to nearest integer)

(B)

set the following values in the formula

20.05/2 = 2.576 Z3 = 1.64 0 = 15 Jo = 50 Mi = 30

we get

sample size n =

= [2 * (2.576 +1.64)2 * 15²/(50 – 30) = 7998.5952/400 = 19.996 = 20 (rounded to nearest integer)

(C)

set the following values in the formula

20.05/2 = 1.96 Z3 = 1.28 0 = 0.5 Mo = 1.52 Mi = 1.30

we get

sample size n =

= [2 * (1.96 + 1.28)2 * 0.521/(1.52 – 1.30) = 5.2488/0.0484 = 108.446 = 108 (rounded to nearest integer)

(D)

set the following values in the formula

20.10/2 = 1.64 Z3 = 0.84 0 = 100 Mo = 1100 Mi = 1000

we get

sample size n =

= [2 * (1.64 +0.84)2 * 100°)/(1100 – 1000) = 123008/10000 = 12.3 = 12 (rounded to nearest integer)