Question

An article stated, "Surveys tell us that more than half of America's college graduates are avid readers of mystery novels." Let p denote the actual proportion of college graduates who are avid readers of mystery novels. Consider a sample proportion p̂ that is based on a random sample of 225 college graduates.

(a) If p = 0.5, what are the mean value and standard deviation of p̂? (Round your answers to four decimal places.)

mean
standard deviation

If p = 0.6, what are the mean value and standard deviation of p̂? (Round your answers to four decimal places.)

mean
standard deviation

Does p̂ have approximately a normal distribution in both cases? Explain.

Yes, because in both cases np > 10 and n(1 − p) > 10.No, because in both cases np < 10 or n(1 − p) < 10.    No, because when p = 0.5, np < 10.No, because when p = 0.6, np < 10.

(b) Calculate P(p̂ ≥ 0.6) for p = 0.5. (Round your answer to four decimal places.)


Calculate P(p̂ ≥ 0.6) for p = 0.6.


(c) Without doing any calculations, how do you think the probabilities in Part (b) would change if n were 400 rather than 225?

When p = 0.5, the P(p̂ ≥ 0.6) would decrease if the sample size was 400 rather than 225. When p = 0.6, the P(p̂ ≥ 0.6) would decrease if the sample size was 400 rather than 225.When p = 0.5, the P(p̂ ≥ 0.6) would decrease if the sample size was 400 rather than 225. When p = 0.6, the P(p̂ ≥ 0.6) would remain the same if the sample size was 400 rather than 225.    When p = 0.5, the P(p̂ ≥ 0.6) would remain the same if the sample size was 400 rather than 225. When p = 0.6, the P(p̂ ≥ 0.6) would decrease if the sample size was 400 rather than 225.When p = 0.5, the P(p̂ ≥ 0.6) would remain the same if the sample size was 400 rather than 225. When p = 0.6, the P(p̂ ≥ 0.6) would remain the same if the sample size was 400 rather than 225.

Answer 1