According to a survey, the average cost of a fast-food meal (quarter-pound cheeseburger, large fries, medium soft drink, excluding taxes) in a certain city is $6.82. Suppose this figure was based on a sample of 27 different establishments and the standard deviation was $0.37. Construct a 95% confidence interval for the population mean cost for all fast-food meals in the city. Assume the costs of a fast-food meal in the city are normally distributed. Using the interval as a guide, is it likely that the population mean is really $6.50? Why or why not?