Question

Problems $29-38$each include a normal probability plot and either a frequency histogram or a stem-and-leaf diagram for a set of sample data. The intent is to use the sample data to perform a hypothesis test for the mean of the population from which the data were obtained. In each case, consult the graphs provided to decide whether to use the $z-$test, the $t-$test, or neither: Explain your answer.

29. The normal probability plot and histogram of the data are depicted in Fig. $9.23$; $\sigma$is known.

Short answer

The sample size is large and $\sigma$is known.

Step-by-step solution

Step 1. Given Information 

A graph with plotting:

Step 2. Observing the graph

Here the sample size is large and also $\sigma$is known. So, using the $z-$test appears to be reasonable. But normal probability plot indicates that there may be outliers in the data. So it is necessary to check whether they are potential outliers; if they are, then to check whether the outliers are removable or not. If the potential outliers are not removable, one may use any nonparametric method instead of $z-$test as the variable under consideration is roughly symmetric.