Z-Tests - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Math Apps : Gradeable Apps : MathApps/Gradeable/ZTest

Z-Tests

Gradeable Example

A company produces metal discs with a mean weight of grams and standard deviation ofgrams.

 

Suppose that the company takes a sample of size 50 and finds that the sample mean is.

 

Assuming a significance level of 95%, is the company correct in accepting the null hypothesis that the sample does not have different weights on average than the population of metal discs?

 

 

 

 

Background

The Z-test is used to compare means of two distributions with known variance. One sample Z-tests are useful when a sample is being compared to a population, such as testing the hypothesis that the distribution of the test statistic follows a normal distribution. Two-sample Z-tests are more appropriate for comparing the means of two samples of data.

 

Requirements for the Z-test:

• 

The mean and standard deviation of the population distribution are known.

• 

The mean of the sample distribution is known.

• 

The variance of the sample is assumed to be the same as the population.

• 

The population is assumed to be normally distributed

• 

The population size is over 30

 

In cases where the population variance is unknown, or the sample size is less than 30, the Student's t-test  may be more appropriate.

 

To calculate a Z-test statistic, the following formula can be used:

 

z = xμSE,

 

z = xμσn,

 

where x is the sample mean, m is the population mean, and SE is the standard error, which can be calculated using the following formula:

 

SE = σn,

 

where s is the population standard deviation and n is the sample size.

 

For each significance level, α, the Z-test has a critical value. For example, the significance level α = 0.01, has a critical value of 2.326. If the Z-test statistic is greater than this critical value, this may provide evidence for rejecting the null hypothesis.

 

 

More MathApps

MathApps/ProbabilityAndStatistics

MathApps/Gradeable