The coronavirus epidemic has turned us all become statisticians. We’re always double-checking the figures, speculating on how the epidemic will play out, and speculating on when the “peak” will occur. And it’s not only us that develop hypotheses; the media thrives on it as well. What further theories can we make concerning the coronavirus? Are adults more likely to be impacted by the coronavirus outbreak? All of these questions may bring back past knowledge on the principles of Z-Testing if you’re a statistician. In this blog we are going to tell you the What is Z-Test, so read this full blog to get the complete information.
What is Z-Test?
A Z-test is a statistical test in which the test statistic’s distribution may be approximated by a normal distribution under the null hypothesis. The mean of a distribution is tested using Z-tests. In statistics, the Z Test is a hypothesis test that is used to see if the computed means of two samples are different when standard deviations are provided and the sample is big. In order to execute an appropriate z-test, the test statistic is expected to have a normal distribution, and nuisance factors.
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Procedure
Z = (x – μ) / ơ
Where
X holds any value from the population
μ = population mean
ơ = population standard deviation
Z = (x – x_mean) / s
Where
x = holds any value from the sample
x_mean = sample mean
s = sample standard deviation
Understanding Z-Tests
The z-test is a hypothesis test with a regularly distributed z-statistic. The z-test is best utilised for samples with more than 30 because, according to the central limit theorem, samples with more than 30 samples are assumed to be approximately regularly distributed. TWhen doing a z-test, the null and alternative hypotheses, as well as the alpha and z-score, should all be presented. After that, the test statistic, findings, and conclusion should be computed. A z-score, also known as a z-statistic, is a number that reflects how many standard deviations a z-test score is above or below the mean population.
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Example
There are 30 students selected as a part of a sample team to be surveyed to see how many pencils were being used in a week. Determine the z-test score for the 3rd student of based on the given responses: 3, 2, 5, 6, 4, 7, 4, 3, 3, 8, 3, 1, 3, 6, 5, 2, 4, 3, 6, 4, 5, 2, 2, 4, 4, 2, 8, 3, 6, 7.
Given,
x = 5, since the 3rd student’s response, is 5
Sample size, n = 30
Sample mean, = (3 + 2 + 5 + 6 + 4 + 7 + 4 + 3 + 3 + 8 + 3 + 1 + 3 + 6 + 5 + 2 + 4 + 3 + 6 + 4 + 5 + 2 + 2 + 4 + 4 + 2 + 8 + 3 + 6 + 7) / 30
Mean = 4.17
Now, the sample standard deviation can be calculated by using the above formula.
ơ = 1.90
Therefore, the z-test score for the 3rd student can be calculated as,
Z = (x – x ) / s
Z = (5 –17) / 1.90
Z = 0.44
Therefore, the 3rd student’s usage is 0.44 times the standard deviation above the mean usage of the sample i.e. as per z- score table, 67% students use fewer pencils than the 3rd student.
What Are The Types Of Z-Tests?
There are two types of Z -test:
- Paired z-test
- Related z-test
Z-tests for single proportion are used to test a hypothesis on a specific value of the population proportion.For difference of proportions, Z test is used to test the hypothesis when two populations have the same proportion.
Conclusion
In last, I hope this blog sufficient enough to provide the complete information about What is Z-Test?.
