1. As the degrees of freedom increase, what happens to the surprise values of Student t?

 

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© 1999, Duxbury Press. alt="transpcr.gif (812 bytes)"> Surprise Values of t for the Slope

Surprise values for the Student t for the slope are the same as any other surprise values for Student t. The same graph we have seen several times before applies here as well. We have estimated two unknown values for the line--the intercept and the slope--so the degrees of freedom equal n - 2. Use the graph below to find the surprise values for different numbers of degrees of freedom. transpcr.gif (812 bytes)  

Move the slider to change the degrees of freedom.
 
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  There are fifteen observations in the Statistical Knowledge Quiz data, so df = 15 - 2 = 13. What are the surprise values of Student t in that case?  
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© 1999, Duxbury Press. reporting of errors, typos, etc. --> File:
© 1999, Duxbury Press. The sampling distribution of the slope allows us to identify surprising values. In this case, values of the slope more extreme than +/- .4 are extremely rare and values more extreme than +/- .3 are surprising.  
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© 1999, Duxbury Press. LIGN=CENTER VALIGN=MIDDLE>2 3 4 5 6 7 8 9 10 Stress 2.5 5 10 15 17.5 20 25 30 35 40 FailTime 63 58 55 61 62 37 38 45 46 19

Move the line up and down by dragging the box or change the slope by clicking and dragging anywhere else so that the line represents all the observations. Try to place the line so that it is closest to all the observations.

Based on your line, do you think there is a positive, negative, or no relationship between Stress and FailTime?

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Biology

Ott (1993) presents this example on p. 452: Fifteen male volunteers ate a low-cholesterol diet for four weeks. Below are the ages and the reduction in cholesterol (in mg per 100 ml of blood serum) for each participant:
Participant 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Age 45 43 46 49 50 37 34 30 31 26 22 58 60 52 27
Reduce 30 52 45 38 62 55 25 30 40 17 28 44 61 58 45

Move the line up and down by dragging the box or change the slope by clicking and dragging anywhere else so that the line represents all the observations. Try to place the line so that it is closest to all the observations.

Based on your line, do you think there is a positive, negative, or no relationship between Age and Reduce?

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© 1999, Duxbury Press. a dieter's age and the amount of cholesterol reduced?

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© 1999, Duxbury Press. al">File: