Recently, a case of salmonella (bacterial) poisoning was traced to a particular brand of ice cream bar, and the manufacturer removed the bars from the market. Despite this response, many consumers refused to purchase J brand of ice cream bars for some period of time after the event (McClave, personal consulting). One manufacturer conducted a survey of consumers 6 months after the out- f break. A sample of 244 ice cream bar consumers was contacted, and 23 respondents indicated that they would not purchase ice cream bars because of the potential for food J poisoning.
a. What is the point estimate of the true fraction of the entire market who refuse to purchase bars 6 months after I the outbreak?
b. Is the sample size large enough to use the normal I approximation for the sampling distribution of the estimator of the binomial probability? Justify your response.
c. Construct a 95 % confidence interval for the true proportion of the market who still refuses to purchase ice cream bars 6 months after the event.
d. Interpret both the point estimate and confidence interval in terms of this application.