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 fourstep hypothesis testing
process verifies this.
Next month, Kohl will be challenged with a slightly
more sophisticated set of data.
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