What is a 'ZTest'
A ztest 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 ztest to be performed.
BREAKING DOWN 'ZTest'
A onesample location test, twosample location test, paired difference test and maximum likelihood estimate are examples of tests that can be conducted as ztests. Ztests are closely related to ttests, but ttests are best performed when an experiment has a small sample size. Also, ttests assume the standard deviation is unknown, while ztests 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 ztest is a hypothesis test in which the zstatistic follows a normal distribution. The ztest 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 ztest, the null and alternative hypotheses, alpha and zscore should be stated. Next, the test statistic should be calculated, and the results and conclusion stated.
OneSample ZTest 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 twotailed 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.
The value for z is calculated by subtracting the value of the average daily return selected for the test, or 1% in this case, from the observed average of the samples. Next, divide the resulting value by the standard deviation divided by the square root of the number of observed values. Therefore, the test statistic is calculated to be 2.83, or (0.02  0.01) / (0.025 / (50)^(1/2)). The investor rejects the null hypothesis since z is greater than 1.96 and concludes the average daily return is greater than 1%.

TTest
A statistical examination of two population means. A twosample ... 
Sampling
A process used in statistical analysis in which a predetermined ... 
Null Hypothesis
A null hypothesis is a type of hypothesis used in statistics ... 
Sample
A sample is a smaller, manageable version of a larger group. ... 
Standard Error
Standard error is the approximate standard deviation of a statistical ... 
T Distribution
A T distribution is a type of probability function that is appropriate ...

Investing
Why Standard Deviation Should Matter to Investors
Think of standard deviation as a thermometer for risk, or better yet, anxiety. 
Investing
Optimize your portfolio using normal distribution
Normal or bell curve distribution can be used in portfolio theory to help portfolio managers maximize return and minimize risk. 
Investing
5 Ways To Measure Mutual Fund Risk
These statistical measures help investors understand investment risk and how it relates to returns. 
Trading
Improve your investing with Excel
Excel is a useful tool to assist with investment organization and evaluation. Find out how to use it. 
Investing
PRHSX: Risk Statistics of Health Sciences Mutual Fund
Examine the risk metric of the T. Rowe Price Health Sciences Fund. Analyze beta, capture ratios and standard deviation to assess volatility and systematic risk. 
Investing
Redefining Investor Risk
Changing the way you think about time and risk can change the way you invest. 
Investing
Find the right fit with probability distributions
Discover a few of the most popular probability distributions and how to calculate them. 
Investing
Calculating Tracking Error
Tracking error is the difference between the return on a portfolio or fund, and the benchmark it is expected to mirror (or track). 
Insights
Which Consumer Genetic Tests Are FDAApproved?
Now you can get some genetic tests without going to a doctor. Should you? 
Personal Finance
Top 20 Countries With the Highest GMAT Scores
A total of 42 countries had higher average scores than the U.S. in the last testing year.

What percentage of the population do you need in a representative sample?
Learn about representative samples and how they are used in conjunction with other strategies to create useful data with ... Read Answer >> 
What are the advantages of using a simple random sample to study a larger population?
Learn how simple random sampling works and what advantages it offers over other sampling methods when selecting a research ... Read Answer >> 
What are the advantages and disadvantages of using systematic sampling?
Learn about the primary advantages and disadvantages of using a systematic sampling method when conducting research of a ... Read Answer >> 
What is the difference between standard deviation and average deviation?
Understand the basics of standard deviation and average deviation, including how each is calculated and why standard deviation ... Read Answer >> 
What are the disadvantages of using a simple random sample to approximate a larger ...
Learn what a simple random sample is, how researchers use it as a statistical tool and the disadvantages it carries when ... Read Answer >> 
What's An Example of Stratified Random Sampling?
Stratified random sampling divides a population into subgroups or strata, whereby the members in each of the stratum formed ... Read Answer >>