Vol. 8, No. 8 August 2006
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 Quality Quiz from Professor Cleary Congratulations: "No" is correct. Click here for a more complete video explanation The t value of 5.06 has nothing to do with time, of course. It is instead the statistic used to answer the question, "Is there a relationship between X and Y?" Once again we have entered the world of hypothesis testing. Here's what Kohl should have been explaining to Hal: Hypothesis testing for scattergrams (linear regression): Step 1 Interpretation: The null hypothesis (Ho) is that there is no relationship between X and Y. The alternative (Ha) is that X has an effect on the value of Y. Step 2 Interpretation: We are willing to accept a 1% chance of a Type 1 error, which involves rejecting the null hypothesis when it is in fact true. Step 3 Calculate the appropriate t value to test this hypothesis. Interpretation: • We have assumed that X and Y are not related. Therefore , the hypothetical regression coefficient, must be equal to .0 • The calculated value for b1, which is an estimate for , is equal to .86. • The amount of error that occurred in calculating b is .1699. • The appropriately calculated t is or 5.06. • The larger the calculated t, the more likely it is that we will reject the null hypothesis = 0. • If we reject the null, the conclusion is that there is a relationship between X and Y. Step 4 Compare the calculated t to the tabular t, to decide whether to accept or reject the null hypothesis. In this case, the tabular t is 3.355, and the calculated t is 5.06. Since the calculated t is greater than the tabular t, we must reject that = 0, and therefore conclude that X does indeed have an effect on the value of Y. Looking at Kohl's data, it seems intuitively obvious that X (tons mixed) affects Y (cost). The four-step hypothesis testing process verifies this. Next month, Kohl will be challenged with a slightly more sophisticated set of data. Click here to register to win a free Quality Gamebox program. Copyright 2006 PQ Systems. Please direct questions or problems regarding this web site to the Webmaster.