The effect of sample size. TheSRSof size 200 described in the previous exercise finds that 100 of the 200 respondents are concerned about nutrition.We wonder if this is reason to conclude that the percent in your area is higher than the national 40%.

(a) Find the probability that X is 100 or larger if p = 0.4 is true. If this probability is very small, that is reason to think that p is actually greater than 0.4 in your area.

(b) In Exercise 5.60, you found P(X ≥ 10) for a sample of size 20. In (a), you have found P(X ≥ 100) for a sample of size 200 from the same population. Both of these probabilities answer the question “How likely is a sample with at least 50%

successes when the population has 40% successes?” What does comparing these probabilities suggest about the importance of sample size?