Student Solutions Manual Applied Statistics and Probability for Engineers, Fifth Edition

CHAPTER 8

Section 8-1

8-1      a)   The confidence level for is determined by the value of z₀ which is 2.14. From Table III, Φ(2.14) = P(Z <2.14) = 0.9838 and the confidence level is 2(0.9838 − 0.5) = 96.76%.

b)   The confidence level for is determined by the by the value of z₀ which is 2.14. From Table III, Φ(2.49) = P(Z < 2.49) = 0.9936 and the confidence level is 2(0.9936-0.5) = 98.72%.

c)   The confidence level for is determined by the by the value of z₀, which is 2.14. From Table III, Φ(1.85) = P(Z < 1.85) = 0.9678 and the confidence level is 93.56%.

8-3      a)   A z_α = 1.29 would give result in a 90% one-sided confidence interval.

b)   A z_α = 1.65 would give result in a 95% one-sided confidence interval.

c)   A z_α = 2.33 would give result in a 99% one-sided confidence interval.

8-5      a)   Sample mean from the first confidence interval = 38.02 + (61.98−38.02)/2 = 50

Sample mean from the second confidence interval = 39.95 + (60.05−39.95)/2 = 50

b)   The 95% CI is (38.02, 61.98) and the 90% CI is (39.95, 60.05). The higher the confidence level, the wider the CI.

8-7      a)   Find n for the length of the 95% CI to be 40. Z_a/2 = 1.96     1/2 length = (1.96)(20)/     39.2 = ...