Question

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