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Z-tests are used to check if the means of two populations are different given that the underlying data follows a normal distribution. Many statistics students have issues with solving assignment questions based on Z-tests. Some of them don't understand when to run the test while others are unacquainted with operating SPSS correctly. And while they always have time to consult their lecturers to understand the topic better, the lecturers might just go over the same points as they did in class. But that doesn't mean that they have to struggle with their assignments.
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The Z-Test Explained Explicitly By Our Statisticians
What Is a Z-test?
As already hinted above, a Z-test is a type of hypothesis test that helps researchers to determine whether results from a test are valid or should be repeated. It basically compares the means of two populations to see if they're different or not, provided that the data being used follows a normal distribution, and the population variance is known. A Z-test can only be run under certain conditions, which are:
- When your sample size exceeds 30. Otherwise, you'll opt for a t-test.
- Your data must be normally distributed.
- The data used must have been randomly selected from the population, which each entry having an equal chance of being selected.
- Data points should be independent. That is, no data should affect the other.
- The sample sizes should be equal, if possible.
What is a Z-score?
A Z-score, also called a Z-statistic, is the number obtained after conducting a Z-test. It indicates the number of standard deviations above or below the mean population the score derived from a Z-test is. If you're asking, "What does the z-statistic tell you," the answer is simple. A Z-statistic of 0 indicates that the mean score and data point's score are identical. If the value is 1, it's one standard deviation above the mean. A negative Z-statistic shows how many standard deviations the score derived from the test is below the mean.
How Do You Solve Z-tests Step By Step?
If you want to run a Z-test, you must follow the following steps to ensure that you don't go wrong at any stage:
- Define the null and alternative hypotheses
- Choose an alpha level
- Choose the critical value of Z using a Z table
- Compute the Z-test statistic ( you can use your hand or SPSS)
- Compare the value obtained in the step above (Z-statistic/Z-score) with the critical Z value and decide whether to accept or reject the null hypothesis defined above
What Is The Difference Between a Z-test and a T-test?
While they're often closely related, t-tests are run when the sample is small, typically less than 30. Another difference is that Z-tests assume that the standard deviation is known while t-tests assume that it's unknown. Therefore, a t-test is usually valid where the Z-test doesn't fit.
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Familiarity with When Z-tests are Appropriate
Z-tests are only conducted under certain circumstances, which may be confusing, especially when the researcher/student has to choose between a Z-test and a t-test. But our experts have conducted several hypothesis tests under myriads of circumstances. Therefore, they understand everything about Z-tests.
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