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Members at a popular fitness club currently pay $40 per month to be a member of the club. The owner of the club wants to raise the fee to $50 but is concerned that some members will quit if the fee increases. To investigate, the owner plans to survey a random sample of the members and construct a 95% confidence interval for the proportion of all members who would quit if the fee was increased to $50.
(a) Explain the meaning of "95% confidence" in the context of the study.
(b) After the owner conducted the survey, he calculated the confidence interval to be 0.18 +/- 0.075. Interpret this interval in the context of the study.
(c) According to the club's accountant, the fee increase will be worthwhile if fewer than 20% of the members quit. According to the interval from part (b), can the owner be confident that the fee increase will be worthwhile? Explain.
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