Question

A Internet provider has implemented a new process for handling customer complaints. Based on a review of customer complaint data for the past 2 years, the mean time for handling a customer complain was 27 minutes. Three months after implementing the plan, a random sample of the records of 50 customers who had complaints produced the following response times. Use the 50 data values to determine if the new process has reduced the mean time to handle customer complaints. 32.3 26.9 25.4 32.9 27.7 32.2 24.8 20.5 30.4 21.3 25.9 27.1 19.2 28.4 18.0 33.1 31.1 21.9 33.4 24.3 25.5 29.6 32.7 21.3 31.8 27.6 17.4 26.9 18.9 28.6 23.5 21.6 20.1 30.9 26.8 28.7 24.6 21.5 21.9 28.3 24.1 28.9 29.8 27.1 23.8 25.3 30.7 27.2 19.0 30.0

a. Estimate the mean time for handling a customer complaint under the new process using a 95% confidence interval.

b. Is there substantial evidence (a  .05) that the new process has reduced the mean time to handle a customer complaint?

c. What is the population about which inferences from these data can be made?

Answer 1

Answer:

a) The mean time for handling a customer complaint under the new process using 95% confidence level is between 25.0 min. and 27.5 min.

b) there is no substantial evidence (in 95% confidence level) that the new process has reduced the mean time to handle a customer complaint.

c) The population about which inferences from these data can be made is the people following the new implemented plan when handling customer complaints.

Step-by-step explanation:

the random sample of the response times of 50 customers who had complaints has

size=50

mean≈26.218

standard deviation ≈4.42

a. Confidence interval can be estimated using the formula:

M±$\frac{z*s}{\sqrt{N} }$ where

• M is the sample mean (26.22)
• z is the corresponding z-score for the 95% confidence interval (1.96)
• s is the sample standard deviation (4.42)
• N is the sample size (50)

When we put the numbers in the formula, mean time for handling a customer complain under the new process using 95% confidence interval is:

26.22±$\frac{1.96*4.42}{\sqrt{50} }$≈ 26.22±1.225 i.e. between 25 and 27.45

b. According to the customer complaint data for the past 2 years, the mean time for handling a customer complaint was 27 minutes. After the plan, estimated mean time for handling customer complaint is between 25.0 min. and 27.5 min. with 95% confidence. Since 27 min. is within this interval, we can conclude that there is no substantial evidence (in 95% confidence level) that the new process has reduced the mean time to handle a customer complaint.

c. The population about which inferences from these data can be made is the people following the new implemented plan when handling customer complaints.