Consider the following scenario. Suppose 100 randomly selected customers were as
ID: 3058166 • Letter: C
Question
Consider the following scenario. Suppose 100 randomly selected customers were asked to rate a particular service they recently had on a 0 to 10 scale. The sample mean ( x ) was found to be 7.3. Assume the population standard deviation is known to be sigma= 0.8.
a. A customer relations manager computes the 95% confidence interval for the mean satisfaction as 7.3(plus or minus)1.96(0.8). A common mistake was made here. What is it?
b. The manager fixes the mistake in part (a). After constructing the correct interval, the manager states, “I am 95% confident that the sample mean falls between 7.14 and 7.46.” What misinterpretation is the manager making?
Explanation / Answer
Consider the following scenario. Suppose 100 randomly selected customers were asked to rate a particular service they recently had on a 0 to 10 scale. The sample mean ( x ) was found to be 7.3. Assume the population standard deviation is known to be sigma= 0.8.
a. A customer relations manager computes the 95% confidence interval for the mean satisfaction as 7.3(plus or minus)1.96(0.8). A common mistake was made here. What is it?
b. The manager fixes the mistake in part (a). After constructing the correct interval, the manager states, “I am 95% confident that the sample mean falls between 7.14 and 7.46.” What misinterpretation is the manager making?