Reading 11, Practice Problem 3 (b) Page 612 of printed copy

why they have used z = (x bar - mu)/(sigma/sqrt(n)) rather than z = (x bar- mu)/sigma

In the following chapters, they are denoting it as the test statistic. What is the difference between standardizing and determining test statistic? The calculated z value using both formulas use z table. Which one will be applicable in which situation?

The first formula uses the standard error, and is the test statistic for an hypothesis test about the mean of the population.

The second formula uses the standard deviation, and is the test statistic for an hypothesis test about a (single) random data point in the population.