When the variances are known and the sample size is high, a z test is used to assess whether two population means are different.
In simple language, a hypothesis test in which the z-statistic follows a normal distribution is known as a z-test.In this article, we’ll talk about Z-test and how it can be calculated using Google Sheets.
A z-statistic, often known as a z-score, is a numerical representation of the z-test result. Z-tests are similar to t-tests, however, t-tests are more appropriate for experiments with small sample sizes.
The standard deviation is known in Z-tests, whereas it is unknown in t-tests.
The z-test is a hypothesis test that uses a normal distribution for the z-statistic. Because the central limit theorem states that as the number of samples increases, the samples are assumed to be nearly normally distributed, the z-test is best employed for samples with more than 30.
The null and alternative hypotheses, as well as the alpha and z-score, should all be reported when doing a z-test. The test statistic should next be computed, followed by the findings and conclusion.
A z-statistic, also known as a z-score, is a number that indicates how many standard deviations a score produced from a z-test is above or below the mean population.
The Z.TEST function is handy for numerous analyses as a financial analyst. For example, we can select whether or not to invest in a certain stock based on its average daily return.
Z Test Formula
The parameters to the Z.TEST function are as follows:
|a. Array (required argument): This is the data range or array against which we’ll be testing x. The array is a collection of numbers that will be used to test the sample mean hypothesis.|
|b. X (optional argument): This is the sample that has been proposed. It is the value that will be put to the test.|
|c. Sigma (optional argument): If the standard deviation of the population is known, this represents it. The sample standard deviation is used if this parameter is omitted.|
How do you compute the z-score?
Google Sheets provides a simple method for determining the Z-score: Z.TEST (). You must combine the distribution’s range and the cell containing the specific number in this formula:
If you want to copy the formula by dragging the box to the lower-right corner of the blue highlighter in Google Sheets, add $ signs to prevent it from changing. Our data, for example, range from A2 to A100. On A3, we want to calculate the Z-score. After that, the formula may be expressed as follows:
This is how the column now looks:
Things to Keep in Mind When Using the Z TEST Excel Function
1. When the underlying population mean is 0, Z.TEST indicates the likelihood that the sample means will be greater than the observed value AVERAGE(array). If AVERAGE(array) x, Z.TEST will return a value larger than 0.5 due to the symmetry of the normal distribution.
2. #VALUE! error -When the value of x or sigma is non-numeric, this occurs.
3. #NUM! Error- When the sigma parameter is set to zero, an error occurs.
4. #N/A error – When the given array is empty, this event occurs.
5. #DIV/0! Error – Occurs when:
- The sigma is not specified, and the array’s standard deviation is 0.
- There is just one value in the supplied array.
When should you use the z-test?
In general, z-tests are employed when the sample size is big (n > 30), but t-tests are most useful when the sample size is small (n 30). Both procedures assume that the data has a normal distribution, although z-tests are most effective when the standard deviation is known.
How do you tell if the z-test is significant?
The absolute value of the test statistic (|z|) must be larger than or equal to the crucial value 1.96 in order to reach a significant level of 0.05 for a two-sided test (which corresponds to the level 0.025 for a one-sided test).
How many different kinds of z-tests are there?
Two forms of two sample z -tests exist paired z -tests and related z -tests. Paired z -tests compare two equally sized sets of results that are connected (where you test the same group of participants twice or your two groups are similar)
Is z-test parametric or nonparametric?
T-test and z-test on two samples. The two-sample t and z tests are parametric tests used to compare two independent or paired samples.
Actually, The z-score number indicates how many standard deviations you are from the mean. If you have any queries related to this topic feel free to ask in the comment section. We are here to assist you.
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