XtraNet, an Internet service provider (ISP), has experienced rapid growth in the past five years. As a part of its marketing strategy, XtraNet promises fast connections and dependable service. To achieve its objectives, XtraNet constantly evaluates the capacity of its servers. One component of its evaluation is an analysis of the average amount of time a customer is connected and using the Internet daily. A random sample of 12 customer records shows the following daily usage times, in minutes:

268 336 296 311 306 335 301 278 290 393 373 329

a. Using the sample data, compute the best point estimate of the population mean for daily usage times for XtraNet’s customers.

b. The managers of Xtranet’s marketing department would like to develop a 99% confidence interval estimate for the population mean daily customer usage time. Because the population standard deviation of daily customer usage time is unknown and the sample size is small, what assumption must the marketing managers make concerning the population of daily customer usage times?

c. Construct and interpret a 99% confidence interval for the mean daily usage time for XtraNet’s customers.

d. Assume that before the sample was taken, Xtranet’s marketing staff believed that mean daily usage for its customers was 267 minutes. Does their assumption concerning mean daily usage seem reasonable based on the confidence interval developed in part c?