EXAMPLE 13 Checking whether the conditions are met for the interval for

Never assume normality unless it is indicated or evidence for it exists.

For each of the following, we are taking a random sample from a population with unknown. Determine whether the conditions are met for constructing the indicated interval for . If not, explain why not.

  1. Confidence level 99%, , ,
  2. Confidence level 95%, , , , normal population

Solution

  1. The sample size is not large , and we are not told that the population is normal. Therefore, the conditions are not met for the interval for . It is not okay to construct the interval.
  2. Again the sample size is not large, but this time we are told that the population is normal. Thus, the conditions are met for the interval for . It is okay to construct the interval.

NOW YOU CAN DO

Exercises 9–12.