A study was conducted to investigate whether a new drug could significantly reduce pan in people with arthritis. From a group of 500 people with arthritis 250 were randomly assigned to receive the drug (group 1) and the remaining people were assigned a placebo (group 2). After one month of treatment, 225 people in group 1 reported pain relief and 150 people in group 2 reported pain relief Let Pe represent the combined (or pooled) sample proportion for the two samples. Have the conditions for inference for testing the difference in population proportions been met?

a. No. The people in the study were not selected at random.
b. No. The number of people in the study was too large compared with the size of the population.
c. No. The normality of the sampling distribution cannot be assumed because Pe times each sample size is not sufficiently large.
d. No. The normality of the sampling distribution cannot be assumed because (1 - Pe) times each sample size is not sufficiently large.
d. Yes. All conditions for inference have been met.