Question

13. Nationally, 65.4% of post-secondary institutions are classified as two-year schools. I take a random sample of 80 institutions in California and find that 68.8% of these institutions are classified as two-year schools. Steve sees this and thinks that the proportion of two-year schools in California must be higher than in the rest of the country. His friend, Emma, calculates the probability of observing a ?̂≥ 0.688 if the proportion in California is the same as the rest of the country to be 0.261 and argues that we don’t have enough reason to support Steve’s thought. Assuming Emma’s calculated the probability correctly, who should we believe?

a. We should believe Steve because the sample of 80 California schools was a random sample.

b. We should believe Steve because the difference between 0.688 and 0.654 is less than 0.05.

c. We should believe Emma because observing a sample proportion of 0.688 or more when the true proportion is 0.654 will happen about 26% of the times, we take a random sample like this.

d. We should believe Emma because the difference between 0.688 and 0.261 is more than 0.05.

Answer 1

c. We should believe Emma because observing a sample proportion of 0.688 or more when the true proportion is 0.654 will happen about 26% of the times, we take a random sample like this.