Question

An insurance company has an online help service for its customers. Customer queries that take more than 5 minutes to resolve are categorized as unsatisfactory experiences. To evaluate the quality of its service, the company take 10 sample of 100 calls each while the process is under control.

Calculate the p⁻ value and Sₚ values and set up control limits so that future sample p values should fall within the control limits 99.7% of the time.

The p⁻ value is ___

Answer 1

To calculate the p value and SΠ value, we first need to determine the values of n (sample size) and x (number of unsatisfactory experiences) from the given information. In this case, the sample size is 10 and the number of unsatisfactory experiences should be 5 or more, which we'll assume to be the worst-case scenario. Using these values, we can calculate p⁻ and Sₚ as p⁻ = 0.05 and Sₚ = 0.0212.

Step-by-step explanation:

To calculate the p value and SΠ value, we first need to determine the values of n (sample size) and x (number of unsatisfactory experiences) from the given information. In this case, the sample size is 10 and the number of unsatisfactory experiences should be 5 or more, which we'll assume to be the worst-case scenario. Using these values, we can calculate p⁻ and Sₚ as follows:

p⁻ = x/n = 5/100 = 0.05

Sₚ = sqrt(p⁻(1-p⁻)/n) = sqrt(0.05(1-0.05)/100) = 0.0212

To set up the control limits so that future sample p values fall within the control limits 99.7% of the time, we use the formula:

p⁻ ± 3Sₚ = 0.05 ± 3(0.0212) = (0.0474, 0.0526)

Therefore, the p⁻ value is 0.05.