EXAMPLE 2 Determining whether the interval for may be used

For the following situations, state whether the confidence interval for the population mean may be used. Assume the population is normally distributed.

  1. The sample size is 30, but the value of is unknown.
  2. The sample size is 30, and the value of is known.

Solution

  1. Even though the population is normally distributed, the value of the population standard deviation is unknown, so the interval may not be used.
  2. Now the value of is known, and the population is normally distributed, so the interval may be used.

NOW YOU CAN DO

Exercises 15–20.