Question 5.17

5.17 The effect of sample size.

The SRS of 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%.

  1. Find the probability that is 100 or larger if is true. If this probability is very small, that is reason to think that is actually greater than 0.4 in your area.
  2. In Exercise 5.8, you found for a sample of size 20. In part (a), you have found 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?

5.17

(a) 0.0019. (b) The larger sample gives a much smaller probability, suggesting a greater ability to detect differences.