Question

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

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.

Short answer

z-test is used.

Step-by-step solution

Step 1. Given Information 

Step 2. Conditions to use z-test

Small Sample size:

If the sample size is less than 15, the z-test procedure is used when the variable is normally distributed or very close to being normally distributed.

Moderate Sample size:

If the sample size lies between 15 and 30, the z- test procedure is used when the variable far from being normally distributed or there is no outlier in the data.

Large Sample size:

If the sample size is greater than 30, the z- test procedure is used without any restriction.

Step 3. Conditions for t-test.

Small Sample size:

• Samples are randomly selected from the population.
• Population follows normal distribution or the sample size is larger.
• The standard deviation is unknown.

Step 4. Explanation.

Here, the sample is selected from the population and the sample size is large. Moreover, the population standard deviation is known and there is no outlier. Thus, distribution of the variable is approximately normal. From the above conditions, it is clear that to use of the z- test procedure is appropriate.