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The following data were acquired from these six physicians with
the focus being on the number of years the physician has been
engaged in research and the number of scientific/medical papers
s/he has
published.                

If one assumes the years of doing research and the number of
publications follow normal frequency distributions, one can analyze
these data and determine the linear least-squares regression line
(equation) relating these two variables. (We realize this is a big
assumption, but let’s just go with it!)

I did this for you and the regression equation becomes:
Y^I = 10.0 + 1.4X and the Pearson
Correlation Coefficient becomes: r = 0.872

First arrange the data as a scatter diagram for public
consumption and on it, place the linear regression line. (Make the
scatter plot as large as possible on the supplied graph paper)
(1,1)

Test the significance of this correlation coefficient. In other
words, at 95% confidence, test the claim that there is a positive
correlation between the number of years of research and the number
of publications.

State the Null and Alternative Hypothesis (1)

Draw the appropriate probability density curve setting up the
problem and state the Rejection Rule. (2)

Perform the test and state your decision? (2)

Another physician at Sick Kids says he has 12 years of
experience in research. If you believe the model, what would be the
expected number of publications for this physician? (1)

“That’s nothing”, claims another physician actively engaged in
research. “I have been here for 25 years and I have published over
50 scientific/medical papers.” Do you believe him? Why or why not?
(1,1)

Determine the Standard Error of the Estimate, S_e.
(1)

Upon reflection, if a number of physicians have 12 years of
scientific research; would it be unusual if the mean number of
publications for these physicians to be more than 30 papers? [You
will need to generate the 95% confidence interval and then decide
whether this mean number of publications is within the interval.]
Place this interval on your scatter diagram and indicate the upper
and lower confidence levels. (2,1)

Now if the CEO at Sick Kids hires a new physician with little or
no research experience, would the CEO believe his/her boasts that,
“After 12 years here at Sick Kids, I will publish more than 50
papers?” Show your result as part of your scatter plot. (2,1)

How many publications per year are expected from the physicians
who are engaged in research and have been with Sick Kids for at
least 5 years? (1)

Is it true that Sick Kids will NOT even consider hiring a
physician/researcher who has fewer than 10 publications? Why or why
not? (1,1)