Q.99 - The Practice of Statistics for AP

Question

The reason we use $t$ procedures instead of $z$ procedures when carrying out a test about a population mean is that

(a) $z$ can be used only for large samples.

(b)$z$ requires that you know the population standard deviation $\sigma$.

(c) $z$ requires you to regard your data as an SRS from the population.

(d) $z$ applies only if the population distribution is perfectly Normal.

(e) $z$ can be used only for confidence intervals.

Step-by-Step Solution

Answer

The reason we use $t$ procedures instead of $z$ procedures when carrying out a test about a population mean is that (c) $z$ requires you to regard your data as an SRS from the population. 

Step-1 Given Information

Given in the question that The reason we use $t$ procedures instead of $z$ procedures when carrying out a test about a population mean is that we have to fin out taht which option is correct.

Step-2 Explanation

There are two tests $z$test and $t$ test. The reason of using the $t$ procedures instead of $z$ test is required to discuss here.

$z$-test and $t$-test are defined as statistical procedures that are used to determine whether the sample mean differs from the population mean or not. It must be noted that $z$-test is preferred to use when the standard deviation of the population is given, and $t$-test is used the standard deviation of the population is not given.

The correct option is (c).