An acting school claims that 71% of its graduates land major acting roles within one year of graduation. A random sample of 50 graduates was surveyed, and 30 of them had landed major roles within one year of graduation. Let p hat = the proportion of the sample who had landed major roles within one year of graduation.
The probability that 60% or fewer graduates land a major acting role within one year of graduating from this school is 0.043. Does this result provide convincing evidence against the school’s claim?
A. Yes, it is expected that at least 60 graduates from this school will land a major role within one year of graduation.
B. Yes, the probability of seeing the sample result is so far from what is expected that the probability of it occurring by chance alone is very unlikely (0.043 < 0.05).
C. No, the difference between the sample proportion and the parameter is 11%, which is greater than 5%.
D. No, the difference between the sample result and what is expected is not extreme enough. The probability of it occurring by chance alone is not unlikely (0.043 < 0.05).