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Acording to the website www.costofwedding.com, the average cost of catering a wedding (with an open bar) is $100 per person. Recently, in a random sample of 40 weddings in the U.S it was found that the average catering cost was $110, with a standard deviation of $12. On the basis of this, a 95% confidence interval for the mean catering cost for a wedding $106 to $114.
1) List all the conditions for constructing the confidence interval and verify that the conditions for a valid confidence interval are met.
2) Explain whether the confidence interval provides evidence that the mean catering cost of a wedding has increased. Be specific about the reasoning of using the confidence interval.
3) A popular wedding magazine states in an article on catering costs that "There is a 95% chance that the catering cost of your wedding will be between $106 and $114 per person." Explain what is wrong with this statement and what is a better statement that correctly interprets the confidence interval.
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