The new director of a local YMCA has been told by his predecessors that the average member has belonged for 8.7 years. Examining a random sample of 15 membership files, he finds the mean length of membership to be 7.2 years, with a standard deviation of 2.5 years. Assuming the population is approximately normally distributed, and using the 0.05 level, does this result suggest that the actual mean length of membership may be some value other than 8.7 years?
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