Using the pbc data set (from the survival library), answer the following questions:

  1. What is the probability of the null hypothesis that the age of the study participants in normally distributed?

  2. Is the proportion of women in the study what would be expected if particpants were selcted randomly from the us population (females = 50.8% of population). What is the p-value associated with that null hypothesis?

  3. Is there a statistically significant difference between the cholesterol levels of men versus women?

  4. Is there a statistically significant relationship between sex and disease stage? You will need to use the “table” command to put these columns (pbc[,c(“sex”,“stage”)]) into a contingency table first.

  5. Is there a statistically significant correlation between serum albumin and serum cholesterol?

  6. Is there a statistically significant correlation between age and cholesterol?

  7. Did you use parametric or non-parametric statistical tests to answer the previous questions? If challenged by a reviewer, how would you justify your choice?
  8. When deciding whether your results were statistically significant, what did you use as your threshold p-value? Why?