Question

The percent defective for parts produced by a manufacturing process is targeted at 4%. The process is monitored daily by taking samples of sizes n = 160 units. Suppose that today’s sample contains 14 defectives. Determine a 88% confidence interval for the proportion defective for the process today. Place your LOWER limit, rounded to 3 decimal places, in the first blank. For example, 0.123 would be a legitimate answer. Place your UPPER limit, rounded to 3 decimal places, in the second blank. For example, 0.345 would be a legitimate entry. Make sure you include the 0 before the decimal.

Answer 1

sample proportion, = 0.0875
sample size, n = 160
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.0875 * (1 - 0.0875)/160) = 0.0223

Given CI level is 88%, hence α = 1 - 0.88 = 0.12
α/2 = 0.12/2 = 0.06, Zc = Z(α/2) = 1.55

Margin of Error, ME = zc * SE
ME = 1.55 * 0.0223
ME = 0.035

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.0875 - 1.55 * 0.0223 , 0.0875 + 1.55 * 0.0223)
CI = (0.053 , 0.122)

Lower limit = 0.053
Upper limit = 0.122