Question 8.79

image 79. Refer to Exercise 77. What if the confidence level is decreased from 95% to some unspecified lower value. Explain whether and how this decrease would affect the following:

  3. Width of the confidence interval
  5. Margin of error

8.1.79

(a) Since is a population characteristic, it stay constant and is unaffected by a decrease in confidence level. (b) The quantity is unaffected by a decrease in confidence level. (c) A decrease in the confidence level will result in a decrease in . The width of the confidence interval . Thus a decrease in will result in a decrease in the width of the confidence interval. (d) The quantity depends only on the sample taken, so it will remain unaffected by a decrease in the confidence level. (e) A decrease in the confidence level will result in a decrease in . Since the margin of error is a decrease in will result in a decrease in the margin of error.