The z-test

Overview

Whenever the normal probability curve is set up as the statistical distribution for testing hypothesis about a population, the z-tests are used. There are 4 types of z test that will be taken up.

Lesson 1: z-test of Hypothesis about a Population Mean Before the z-one population test of hypothesis about a population mean is applied, certain assumptions must be met: (1) The (population standard deviation) is known. (2) The data are either interval or ratio. (3) Only one group is specified. (4) The distributions of the scores follow the normal distribution.

A special table called the z-table is used to facilitate the work on hypothesis testing. These values can be obtained using the table under the normal curve:

The z table | Type / | 0.025 | 0.01 | 0.05 | One-tailed | 1.96 | 2.33 | 1.65 | Two tailed | 2.33 | 2.58 | 1.96 |

Application: In the national level, the average score in the National Secondary Achievement Tests is 485 with a standard deviation of 95. A random sample of 135 freshmen entering the Philippine Normal University shows a mean score of 620. Can we say that the mean of this group comes from a population whose true mean () = 485? or is there a significant difference between the national average score and the mean score of the incoming freshman students of PNU?

Research Question: Is there a significant difference between the average score in NSAT and the mean score of the incoming freshmen of PNU? or

Does the sample of 135 entering students of PNU come from a population with = 485?

Ho: = 485 or

Ho: There is no significant difference between the national average score and the mean score of the incoming freshmen students of PNU.

We are hypothesizing that the true mean of the population from where we drew our sample is 485. This is our null hypothesis.

H1: 485 or

H1: There is a significant difference between the national average score