The customer service manager for the XYZ Fastener Manufacturing Company examined 60 vouchers and found nine vouchers containing errors.Find a 98 percent confidence interval for the proportion of vouchers with errors.
A)[.147 .153]
B)[.080 .220]
C)[.043 .257]
D)[.112 .188]

Question

Quizplus · Accepted Answer

First, we need to calculate the point estimate of the proportion of vouchers with errors:
point estimate = number of vouchers with errors / total number of vouchers
point estimate = 9 / 60 = 0.15

Next, we need to calculate the standard error:
standard error = sqrt[(point estimate * (1 - point estimate)) / sample size]
standard error = sqrt[(0.15 * 0.85) / 60] = 0.047

Using a 98% confidence level, we look up the critical value in a standard normal distribution table. The critical value is 2.33.

Finally, we can calculate the confidence interval:
confidence interval = point estimate +/- (critical value * standard error)
confidence interval = 0.15 +/- (2.33 * 0.047)
confidence interval = [0.043, 0.257]

Therefore, the best choice is C, which gives the confidence interval [0.043, 0.257].

The Customer Service Manager for the XYZ Fastener Manufacturing Company