Z-TEST
The z-test is a hypothesis test to determine if a single observed mean is significantly different (or greater or less than) the mean under the null hypothesis, µhypo when you know the standard deviation of the population.
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It’s a statistical check to see if what you observed is meaningfully different from what you expected, using the knowledge of overall variability in the data.
Z-test is the most commonly used statistical tool in research methodology, with it being used for studies where the sample size is large (n>30).
When to use the z test:
- Normal distribution of data
- All data points are independent
- Standard deviation is known
- Sample Size ≥ 30
- Equal sample variance
Standard deviation for sample distribution = Population Standard Deviation / √n
Types of Z Test in Hypothesis Testing:
- Z-test for Means
- Z-test for Proportions
Steps to Perform a Z-Test for Means:
- State the Hypotheses:
- Null Hypothesis (H₀): Assumes there’s no difference between the sample mean and the population mean .
- Alternative Hypothesis (H₁): Suggests that there is a difference (e.g., the sample mean is not equal to, greater than, or less than the population mean).
One-sample z-test is used to compare the sample mean with the population mean. In other words, it checks whether the sample belongs to the given population using Z-statistics.
Two-Sample Z Test for means:
A Two-Sample Z-Test for Means is a statistical method used to compare the averages (means) of two different groups to see if they are significantly different from each other.
Z Test for Proportions
- Single Proportion: When you want to compare the proportion of a particular outcome in a sample to a known population proportion.
- Two Proportions: When you want to compare the proportions of a particular outcome between two independent groups.
- Z-Test for Means: This test compares the average of a sample to a known population mean, or it compares the means of two different samples to determine if they differ significantly.
- Z-Test for Proportions: This test evaluates if a sample proportion differs from a known population proportion, or if the proportions from two different samples are significantly different from each other.
