Question

8.46 Sample size for tossing a coin. Refer to Exercise 8.39 where we analyzed the 10,000 coin tosses made by John Kerrich. Suppose that you want to design as a study that would test the hypothesis that a coin is fair if versus the alternative that the probability of a head is 0.05. what sample 0.51. Using a two-sided test with a = size would be needed to have 0.80 power to detect this alternative? us

Answer 1

500:-8.39) (a)Number of times tossed acoin n. 10,000 Number of Head (X) = 5067 - 5067 10,000 - 0.5067 Il-p) - 1-0.5067 X= 0.4933 Atst. Level, a=54 -0.05 one sample test of proportion, Standard deviation - JPCI-P3 70-5067(1-0.5067) 0.5067(0.4933) Vo.2499854 07049995 From the normal distribution Za = 1.96 E From z table] E = 0.1995 x - X1.96 VI0.000 E = 0.4995 x 1.96 1100

-0.004995X1.96 20.0097902 Poobability of tread at St. level M = 7+1 on Zda (or) X-9 h 7.12 = 0.4933+ 0.49995 X1.96 (or) 0.4933 - V10,000 0.49995 x 1.96 V10,000 = 0.4933 +0.9097902 (or) 0.4933 -0.0097902 20.5030902, 0.4835098 Hence at St. level, the probability of head is not 0.5 (b). from 95.]. Confidence interval for p = 8 2 7 2 12V P(-1/n Mattom 2012 - 5 m 2412 = 0.4933+ Qu9995x1.96, 0.4933 - out V10,000 - 0.4933 +0.0097902, 0.4933 -0.0097902 0.49995 x 1.96 -0.5030902, 0.4835098

from 95% confidence interval, as calculated range of Probability that is not rejeted is given by T 04.10.025 given by 0.015X100-2.5A 0.4835098<^<.0.5030902 1954. confidence Interval 2.57 2.52 2=1.96 Z=1.96