Question

Example 3.1. A politician claimed that he u ill gain at least 50% of votes in a city election and thereby he will win. However, an expert predicted the politician will lose the election after reviewing his policies thoroughly. To test their conjecture, the expert randomly selected 15 voters to ask whether or not the voters support the politician. 6) assuming the 2. From Example 3.1, find the probabilities α and β for the new rejection region {Y same Ho and Hı distributions

Answer 1

From the given information, p = 50% = 0.50, and n = 15. Point estimate for the true proportion is p = p = 0.50 K, p-50% Hi.. P > 50% 1-p 100 (1-a) % confidence interval for true proportion is | p-AR 95% confidence interval estimate for true proportion is 0.50(1-0.50) 0.50-1.96,/0.50(1-0.50) .0.50+1.96, 050(1-0.50 (0.247,0.753) With 95% confidence, we can conclude that the claim is valid. Since, the confidence interval does not contain zero, we reject the null hypothesis. Therefore, there is enough evidence to conclude that he will gain at least 50% of votes in a city election and there by he will win.