1. Confirm that the luminosities of these quasars (column L in the data frame) are not

Question

consistent with being sampled from a normal distribution using a formal test, and provide a

p-value (or limiting p-value). Confirm that this is also holds for the logarithms of the

luminosities (and provide a p-value).

2. Plot a histogram, and a Q-Q plot (with normal line), of the luminosities. In what manner

does the distribution of this quantity differ from normal?

3. Plot a histogram, and a Q-Q plot (with normal line), of the logarithm-transformed

luminosities. In what manner does the distribution of this quantity differ from normal?

Hint: To save space in your PDF, consider plotting the histogram and Q-Q plots side by side.

You do not have to subdivide by type for questions 1-3.

4. Plot the empirical cumulative distribution functions of the logarithm-transformed

luminosities for type C and type D individually, using two separate curves on the same plot.

Make sure the functions are appropriately sampled. Label the axes informatively, use a

different colour for the two curves, and provide a legend.

5. Use an appropriate two-sample test to test the hypothesis that the luminosities of quasar

sample C and quasar sample D were drawn from the same distribution. State your

conclusion and quote a p-value.

For questions 6-9 below, once again consider all quasars together (not subdivided by type).

6. Calculate the average quasar abundance A (for all quasars) using the above equation.

7. Perform a bootstrap (any version) to estimate a 95% confidence interval on the value of A.

8. Stratify the quasar sample by subdividing it into four luminosity bins: 1 ≤L < 10, 10 ≤L<

100, 100 ≤L < 1000, and 1000's L < 10¹. Then, calculate the estimated value of A and an

associated confidence interval for each of these four groups. Output your results as a table

with five columns: bin minimum L, bin maximum L, estimate of A, lower CI on A, upper Cl on

A. Use an appropriate number of significant figures on all values.

9. Make a plot of your result from the previous question, graphically showing your confidence

intervals as error bars on each binned point. Both the x-axis and y-axis should be

logarithmic (in L and A, respectively).