Quality Quiz from Professor Cleary
"B" is correct.
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Cal Lesterol has missed the mark. The t-statistic is used to test the hypothesis that there is no relationship between X and Y. In rejecting that hypothesis, one assumes that X is a valid predictor of Y. The formula to derive the t-statistic is:
t = -13.70
(Practical Tools for Continuous Improvement: Vol. I, Statistical Tools, PQ Systems, Inc., 2001. Page 307.)
In this case, the t value on Cal Lesterol's printout is -13.70. Since there are 24 data points, the degrees of freedom are 22:
Using an alpha value of .05 (the probability of rejecting the null when the null is true), the tabular t is 2.074 (two tail). Since the absolute value of the calculated t is higher than the tabular t, the null is rejected, and one can assume that X is a predictor of Y.
Cal Lesterol's logical, linguistic response has nothing to do with statistics. Fortunately, his audience paid no attention to the t value, but simply let Cal take his chart back to the quality department for further study.
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