Salmonella in ice cream bars. 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 any brand of ice cream bars for some time after the event (McClave, personal correspondence). One manufacturer conducted a survey of consumers 6 months after the poisoning. A sample of 244 ice cream bar consumers was contacted, and 23 indicated that they would not purchase ice cream bars because of the potential for food poisoning.
a. What is the point estimate of the true fraction of the entire market who refuse to purchase bars 6 months after the poisoning?
b. Is the sample size large enough to use the normal 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 refuse to purchase ice cream bars 6 months after the event.
d. Interpret both the point estimate and confidence interval in terms of this application.
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