Question

1. Consider the following problem of determining the proportion of coffee drinkers that prefer instant coffee. We have a preference test for coffee drinkers. In a sample of fifty coffee drinkers, we find 19 prefer instant coffee. (6) Based on this sample, give a 90% CI for population proportion of coffee drinkers that prefer instant coffee. (h) A coffee executive believes that less than 47% of coffee drinkers prefer instant coffee. Test this claim. Show all of your work

Answer 1

Given 19 50 0.38 Proportion P 0.9 0.1 Critical Value Za 2 1.64485363 + 1.645 90 % Confidence interval is sp + Za2 * VP (1 - 0 )/n Lower limit =- Za/2 * (1-0)/n =0.38-1.645 (0.38*(1-0.38)/50) = 0.2671 Upper limit =Ệ + La2 */p (1-)/n =0.38+1.645 (0.38*(1-0.38)50) = 0.4929 90 % Confidence interval is =0.2671 <p < 0.4929 b) Test hypothesis are Null hypothesis Alternate hypothesis II H:p H:p 0.47 0.47 v Since 0.47 is inside the confidence interval hence fail to reject the null hypothesis