Question

Using samples of 200 credit card statements, an auditor found the following:

Use Table-A.
Sample 1 2 3 4
Number with errors 4 2 5 9
a. Determine the fraction defective in each sample. (Round your answers to 3 decimal places.)
Sample Fraction defective
1 2 3 4 b. If the true fraction defective for this process is unknown, what is your estimate of it? (Round your answer to 1 decimal place. Omit the "%" sign in your response.)
Estimate %
c. What is your estimate of the mean and standard deviation of the sampling distribution of fractions defective for samples of this size? (Do not round intermediate calculations. Round your answers to 3 decimal places.)
Mean Standard deviation d. What control limits would give an alpha risk of .03 for this process? (Do not round intermediate calculations. Round your "z" value to 2 decimal places and other answers to 4 decimal places.)
z = , to
e. What alpha risk would control limits of .047 and .003 provide? (Do not round intermediate calculations. Round your "z" value to the nearest whole number and "alpha risk" value to 4 decimal places.)
z = , alpha risk =
f. Using control limits of .047 and .003, is the process in control?
Yes
No
g. Suppose that the long-term fraction defective of the process is known to be 2 percent. What are the values of the mean and standard deviation of the sampling distribution? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Mean Standard deviation

Answer 1

To determine the fraction defective in each sample, divide the number of credit card statements with errors by the total number of credit card statements in each sample. To estimate the true fraction defective, take the average of the fractions defective from all the samples. The mean of the sampling distribution is equal to the estimated true fraction defective, and the standard deviation can be calculated using the formula sqrt((p * (1-p))/n).

Step-by-step explanation:

In order to determine the fraction defective in each sample, we divide the number of credit card statements with errors by the total number of credit card statements in each sample.

1. Sample 1: Fraction defective = 4/200 = 0.020
2. Sample 2: Fraction defective = 2/200 = 0.010
3. Sample 3: Fraction defective = 5/200 = 0.025
4. Sample 4: Fraction defective = 9/200 = 0.045

To estimate the true fraction defective for this process, we can take the average of the fractions defective from all the samples. Therefore, the estimate is: (0.020 + 0.010 + 0.025 + 0.045)/4 = 0.025 or 2.5%.

The mean of the sampling distribution of fractions defective for samples of this size is equal to the estimated true fraction defective, which is 2.5%. The standard deviation can be calculated using the formula: sqrt((p * (1-p))/n), where p is the estimated true fraction defective and n is the sample size. So, the standard deviation is sqrt((0.025 * (1-0.025))/200) = 0.007.