A data set about speed dating includes "like" ratings of male dates made by the female dates. The summary statistics are

nequals

186,

x overbar

equals5.82,

sequals

2.21.

Use a

0.01

significance level to test the claim that the population mean of such ratings is less than

6.00

.

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. Determine the test statistic and P-value