An accounting firm recently stated:
"The client's mean sales per customer is estimated to be between $14.50 and $28.50. Further this estimate is based on a random sample of 100 customers and was computed using 95% confidence.
Discuss the appropriateness of this statement. What is the correct interpretation of this confidence interval?
Basically just rearrange the sentence to what the client is saying in a better statement
The client's statement can be rearranged as follows for better clarity:
"The mean sales per customer for our client is estimated to fall between $14.50 and $28.50. This estimate is based on a random sample of 100 customers and has a 95% confidence level."
Now let's discuss the appropriateness of this statement and the correct interpretation of the confidence interval:
The statement is appropriate because it provides an estimate of the mean sales per customer for the client. It specifies the range of values within which the true mean is likely to be, based on a random sample and with a confidence level of 95%. The choice of a 95% confidence level is a common practice in statistics and implies that if multiple random samples were taken, 95% of the resulting confidence intervals would contain the true mean.
The interpretation of the confidence interval is that there is a 95% likelihood that the true mean sales per customer for the client lies within the range of $14.50 to $28.50. This means that if we were to randomly select different sets of 100 customers and compute the mean sales for each set, about 95% of those means would fall within this range.
However, it's important to note that the confidence interval does not provide a guarantee that the true mean falls exactly within this range. There is still a small chance, 5% in this case, that the true mean may be outside of the given interval.