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A study comparing hotel rates in Rome and Paris was done using 49 rooms randomly selected from Rome and 50 rooms randomly selected from Paris. The average price for a room in Rome was $202.71 per night with a standard deviation of $45.60, and the average price for a room in Paris was $197.40 per night with a standard deviation of $52.20. Find the 98% confidence interval for the true mean difference between hotel room rates in Rome and Paris. Is there a significant difference between the rates?