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The ideal serving temperature of a particular type of red wine in 15 °C. A food critic is worried that even high-profile restaurants are unaware of this important fact and tend to serve this type of wine at a temperature that is too warm. He randomly selects 8 of the best restaurants, orders a bottle of this wine at each place, and measures the serving temperature with a precision thermometer. The mean temperate in his sample is 16.65 °C and the standard deviation is 1.82 °C. The food critic wishes to conduct a test at the .05 level of significance to see if these results provide evidence that the true mean serving temperature is indeed above 15 °C. If the test statistic exceeds a critical value, he will conclude that he has obtained evidence that this wine is generally served too warm.
What is the critical value he will use?
Provide your answer as a number rounded to 3 decimals.
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