Researchers conducted a randomized controlled trial to determine if Medicine A is better than Medicine B in preventing MIs in women with heart disease over the age of 60. The researchers determined that a sample size of 100 would be necessary to have an 80% probability of detecting a true difference of 10% or larger between the two groups. Alpha was set at 0.05. The study results showed that 10% of the women on Medicine A had an MI and 5% of the women on Medicine B had an MI, with P = 0.30. Select the best statement: [PROVIDE A RATIONALE AND JUSTIFY YOUR ANSWER]
a. Given the null hypothesis is true, there is a 30% chance of obtaining a difference of 5% or larger between the two groups.
b. Given the null hypothesis is true, there is a 30% chance of obtaining a difference of 10% or larger between the two groups.
c. The study's power is 20% to detect a true difference of 10% or larger.
d. The probability that a Type II error occurred is 30%.
e. The probability that a Type I error occurred is 30%.