## What is a ‘Z-Test’

A z-test is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large. The test statistic is assumed to have a normal distribution, and nuisance parameters such as standard deviation should be known for an accurate z-test to be performed.

## Explaining ‘Z-Test’

A one-sample location test, two-sample location test, paired difference test and maximum likelihood estimate are examples of tests that can be conducted as z-tests. Z-tests are closely related to t-tests, but t-tests are best performed when an experiment has a small sample size. Also, t-tests assume the standard deviation is unknown, while z-tests assume it is known. If the standard deviation of the population is unknown, the assumption of the sample variance equaling the population variance is made.

## Hypothesis Test

The z-test is a hypothesis test in which the z-statistic follows a normal distribution. The z-test is best used for greater than 30 samples because, under the central limit theorem, as the number of samples gets larger, the samples are considered to be approximately normally distributed. When conducting a z-test, the null and alternative hypotheses, alpha and z-score should be stated. Next, the test statistic should be calculated, and the results and conclusion stated.

## One-Sample Z-Test Example

For example, assume an investor wishes to test whether the average daily return of a stock is greater than 1%. A simple random sample of 50 returns is calculated and has an average of 2%. Assume the standard deviation of the returns is 2.50%. Therefore, the null hypothesis is when the average, or mean, is equal to 3%. Conversely, the alternative hypothesis is whether the mean return is greater than 3%. Assume an alpha of 0.05% is selected with a two-tailed test. Consequently, there is 0.025% of the samples in each tail, and the alpha has a critical value of 1.96 or -1.96. If the value of z is greater than 1.96 or less than -1.96, the null hypothesis is rejected.

## Z Test FAQ

#### How do you find the Z test?

#### How do you perform a Z test?

#### What is difference between z test and t test?

#### What are the conditions for a two sample z test?

#### Why do we use t test instead of Z test?

#### Why are two sample z procedures hardly ever used?

#### How do you interpret t test results?

## Further Reading

- Cortisol shifts financial risk preferences – www.pnas.org [PDF]
- Financial inclusion and economic growth in OIC countries – www.sciencedirect.com [PDF]
- A cointegration test for market efficiency – search.proquest.com [PDF]
- Adoption of International Financial Reporting Standards (IFRS) to Enhance Financial Reporting in Nigeria Universities – platform.almanhal.com [PDF]
- Optimal capital structure Vs. pecking order theory: A further test – www.clutejournals.com [PDF]
- Financial literacy of freshmen business school students – go.gale.com [PDF]
- Empirical evidence of financial statement manipulation during economic recessions – search.proquest.com [PDF]
- Financial dependence and innovation: The case of public versus private firms – www.sciencedirect.com [PDF]
- Estimating daily volatility in financial markets utilizing intraday data – www.sciencedirect.com [PDF]
- Cashless economy and financial statement reporting in Nigeria – papers.ssrn.com [PDF]