Question 8.75

8.75 Find the power

Refer to the previous exercise. Consider performing a significance test to compare the population proportions for the two studies. Use and a two-sided alternative.

  1. Find the power of the significance test for each of the following population proportions in the new study: (i) 0.77, (ii) 0.79, (iii) 0.81, (iv) 0.83, (v) 0.85, (vi) 0.87, and (vii) 0.89.
  2. Display your results with a graph.
  3. Write a short summary describing what you have found in this exercise.

8.75

(a) (i) 0.99. (ii) 0.82. (iii) 0.31. (iv) 0.03. (v) 0.34. (vi) 0.89. (vii) 1. (c) As the difference between the two proportions gets smaller, the power decreases; if the two proportions are quite different, then the power is quite large.