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.

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