According to a large university, 32% of their graduating class will have full time employment within one month after graduation. The admissions office wants to investigate this claim. They contact an SRS of 300 of the previous semester’s graduates. Let pˆ = the proportion of graduates in this sample who had full time employment within one month of graduation. What is the shape of the sampling distribution of pˆ ? Justify. What are the mean and standard deviation of the sampling distribution of pˆ ? Interpret the standard deviation of the sampling distribution of pˆ . The admissions office finds that only 29% of the 300 graduates in the SRS had full time employment within one month of graduation. Assuming the university’s claim that 32% will have employment is true, find the probability that 29% or less of a sample of 300 have full time employment. Does the admissions office have convincing evidence that the proportion of graduates who have full time employment within one month of graduating is actually lower than 32%? Justify.