The following data set represents the time (in minutes) for a random sample of phone calls made by employees at a company:
(b) Find the sample standard deviation.
(c) Use the t-distribution to construct a 90% confidence interval for the population mean and interpret the results. Assume the population of the data set is normally distributed.
(d) Repeat part (c) assuming that. Compare results.
(b) The sample standard deviation is computed as:
Also, using Excel we find that
(c) The 90% confidence interval for the population mean is given by:
wherecorresponds to the tow-tailed cutoff point of t-distribution, for, and 9 degrees of freedom, which means that
This means that
This means that there’s a 90% chance that the interval (4.463051, 8.603616) contains the actual population mean.
(d) Now we assume that the population standard deviation is known, and is equal to. The 90% confidence interval is this case is equal to:
This means that there’s a 90% chance that the interval (4.712649, 8.354011) contains the actual population mean. This means we have a better estimate for, which makes sense, given that we have more information (the population variance is known).