Z-Tests - Maple Help

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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?






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.



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