# Z-test and its statistical Significance

The below is a guidance note and provides an introduction to this topic. Detailed explanation is available in the Z- test assignment help and Z-test homework help sections.

A Z-test is a statistical test involves hypothesis testing. It is an analytical test in which the distribution of the test statistic under the null hypothesis can be estimated by a normal distribution. Owing to the central limit theorem, we say that many test statistics are approximately normally distributed for samples with large data sets. The Z-test has a single critical value for each significance level. For an instance, in the case of a two-tailed test with 5% confidence level is 1.96. This makes it more convenient than the t-test, which has different critical values for each sample size. Thus, many statistical tests can be easily performed as approximate Z-tests, given that the sample size is large or the population variance known.

If the population variance is not known, it has to be estimated from the sample itself. Additionally, if the sample size is not large ie n < 30, the Student’s t-test may be much more appropriate than the z-test.

In short, a z-test is a statistically prominent test, used to determine the similarity between two population means. However there are two terms which should fulfil the basic conditions of a z-test

(a) the variances are known and

(b) the sample size is large (or more than 30).

It is assumed that the test statistic has a normal distribution. Either of the two terms, standard deviation or variance should be known to perform an accurate z-test. In the absence of both of the two terms, we will have to use the t-test.

## Z-tests and other statistical tests

This portion discusses how the other statistical tests are interconnected with z- test. For additional references access the Z-test assignment help and Z-test homework help section.

Many statistical tests can be conducted as z-tests. Tests like a one-sample location test and two-sample location test, paired difference are examples of tests that can be conducted as z-tests. Z-tests are very closely related to t-tests. However, t-tests are typically used to perform an experiment with a small sample size. Additionally, in t-tests, we assume that the standard deviation is not known. Whereas in z-tests, we assume that it is known. In case the standard deviation of the population is not available, it is assumed that the sample variance equals the population variance.

### Sample Explaining Z-Test

This section discusses an example of a z-test. Many more examples are available under the Z-test assignment help and Z-test homework help section. Let us assume, an investor wants to test if the average daily return of a stock is more than 1%. A simple random sample of 50 observations shows an average return of 2%. Assuming that the standard deviation of the returns is 2.50%. Hence, the null hypothesis is when the mean, is equal to 3%. The alternative hypothesis states the mean return is greater than 3%. Assume that we conduct the test at a 5% confidence interval with a two-tailed test. Consequently, we can say that there are 2.5% of the samples in each tail. The alpha or the z statistic has a critical value between 1.96 and -1.96. If the value of z is more than 1.96 or less than -1.96, we can reject the null hypothesis.

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