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Answer:
<em>a)</em><em> 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. </em>
<em>b) </em><em>there is no substantial evidence</em><em> </em><em>(in 95% confidence level) that the new process has reduced the mean time to handle a customer complaint.</em>
<em>c) </em><em>The population about which inferences from these data can be made is the people following the new implemented plan when handling customer complaints.</em>
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± 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±≈ 26.22±1.225 i.e. between 25 and 27.45
b<em>. </em>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 <em>25.0 min. and 27.5 min. with 95% confidence. </em>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.