The company that makes the popular Red Bull drink is considering the launch of a new Black Bull drink. The Marketing Dept intends to ask a sample of people try the drink and then based on the results determine if it should launch the new drink. The Marketing Dept. decided to set up a booth at the corner of Yonge & Dundas over the Easter long weekend. Anyone who came by the booth was handed a small cup of the drink and were asked if they liked the drink or not. 503 people said they liked the drink out of 910 people.
(a) Construct a hypothesis test so that rejection of the null hypothesis will permit the conclusion that the proportion of population that like the drink is greater than 0.5. Test the hypothesis using test significance level of 0.01 and p-value approach.
(b) Construct a 99% confidence interval for the proportion of the population that likes the drink. The company would want to launch the drink if the proportion is greater than 0.5. Should it launch the drink based on the confidence interval?
(c) Suppose you are writing an executive summary for senior management and at the end of the summary you make this statement: "The poll's margin of error is plus or minus X%, 99 times out of 100". Compute the value of X.