Question

4. A group in favor of freezing production of nuclear weapons believes that the proportion of individuals in favor of a nuclear freeze is greater for those who have seen the movie "The Day After" (population 1) than those who have not (population 2). In an attempt to verify this belief, random samples of size 500 are obtained from each population of interest. Among those who had seen "The Day After", 228 were in favor of a freeze. For those who had not seen the movie, 196 favored a freeze. (a) [1] Set up the appropriate null and alternative hypotheses. (b) (1) Set up the rejection region for this test using a = 0.05. (c) 2 Find the appropriate test statistic. (d) [2] State and interpret your conclusion. (e) (2) Find the p-value for this test. (f) (2) construct a 99% confident interval for the difference between two population proportions

Answer 1

- Let & be the random variable which denotes the individuals in favor of a nuclear freeze who have seen the movie " The Day After". Let y be the random raciable which denotes the individuals in favor of a nuclear freeze who have not seen the movie "The Day After" Sample size, n=500 = x= ny. px-Sample proportion of the individuals in favor of a nuclear freeze who have seen the movie & 228 →py - Sample proportion of the individuals in favor of a nuclear freeze who have not seen the movie x in Xx 500 = 196 500 (a) Null hypothesis (Ho): Px=Py, ie, there is no significant difference in the indevinals an favor of a freeze between who have seen and not seen the movie, versus Alternative hypothesis (Hi): Px> Py. (b) The rejection region when &= 0.05 is, Zeal > Zx ouN(0,1). Spci-p? (ñ + 1 - 2 ) Zcal (px-py)-(Px - Py) where

Here p = nx px + nypy nx + hy. (c) Under the will hypothens, Px=py. here the test statistic is, (px - py) Zcal - UNCO,1). V p (1-6) ( + 1 ) p = nx px + mypy (500x 228) + (500 x 196) nx thy 500 +500 - p = 0.424] Zcal = 22% 500 196 500 150 70.424(1-0,424) Groot woo) Zcal = 2.0476 (d) Zx = 70.05 - 1.64 Zcal > 7x We reject Ho and conclude that Px>Py. (e) P-value for this test is. P(z> to cal) = 1-P(Z = Zcal) = 1-P (2=2.0476) = 0.0202. (6) Aqail. confidence interval for the difference between two population proportions is, (px-py). I Zx ſpx (1-px) + by (1-py) Here @= 0.01 Zx=2.33

hower bound: 2.28 196 [o.uso) (1-0,456) + (0.392) (1-0.392 500 500 500 500 = -0.008 67 Upper bound : (0.456 -0.392) + (2.337 6.450) (1-0,456) (0.392) (1-0,392) 500 500 = 0.1367. .: A nail confidence interval for difference between two population proportion is. [-0.0087, 0.1367].