Q. 34 - Elementary Statistics

Question

The normal probability curve and stem-to-leaf diagram of the data are shown in figure; $\sigma$ is unknown.

Perform Hypothesis test for mean of the population from which data is obtained and decide whether to use z-test, t-test or neither. Explain your answer.

Step-by-Step Solution

Answer

Neither test (z-test or t-test) would be used. But, some statistician would be used t-test because the population standard deviation is unknown and the sample size small.

Step 1. Given Information

Step 2. Consulting plots

From the given plots, it is observed that the distribution of the data is not approximately normally distributed.

Step 3. Explanation

Since the distribution of the data is not normally distributed and the sample size is small, neither test (z-test or t-test) would be used. But, some statistician would be used t-test because the population standard deviation is unknown and the sample size small.