A data set about speed dating includes​ "like" ratings of male dates made by the female dates. The summary statistics are n=195​, x=7.83​, s=2.28. Use a 0.01 significance level to test the claim that the population mean of such ratings is less than 8.00. Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

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