Question

Antal survey conducted among a simple random sample of 1,514 ts show that of American think the vil War (a) Conduct a l othesis test to determine these data provide strong evidence that the majority of the American think the relevant to American poities and politice War is strvant State the appropriate mull and alternative hypotheses. 05 MD 0.5 • Hip-os NDOS • Hoip-0.5 HD > 0 • HD-0.5 H05

Answer 1

: p< 0.5 Hypotheses: To test null hypothesis H. : p=0.5 against alternative hypothesis H Let p denotes the sample proportion and n denotes the sample size. Here, P = 0.5900, n = 1514, standard error = 0.5*(1 – 0.5) P=0.012850 1514 The test statistic can be written as: (p - 0.5) 2 = 0.5*(1-0.5) which under H, follows a standard normal distribution. Decision rule / Rejection region : We reject Ho at 0.05 level of significance if P-value < 0.05 or if zobs < -20.05 = -1.644854 0.4 - 0.3 - >0.2- 0.1- 0.0-, Now, 4 ó Value of test statistic: The value of the test statistic = 7.003828 The critical value = -1.644854 P-value = P(Z < Zobs) = P(Z < 7.003828) = 1.000000 ~ 1.0000 Conclusion: Since p-value > 0.05 and zobs critical = -1.644854, so We fail to reject Ho at 0.05 level of significance Hence, we can conclude that the population proportion is not significantly less than 0.5