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.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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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