Can both of the above tests be applied to the same data? And is it correct?
Yes, both Z-test and T-test can be applied to the same dataset, but it depends on the sample size and population standard deviation availability whether it is correct to do so.
Based on these criteria
Sample Size
Population Standard Deviation (σ)
Distribution Assumption
Usage
Correction (If Needed)
- If the population standard deviation (σ) is unknown, then using a Z-test would be incorrect and a T-test should be used instead.
- If the sample size is small (n < 30), then using a Z-test would be incorrect and a T-test should be used.
-------Both tests are used for hypothesis testing, but they should not be applied to the same data unless the conditions fit both tests. If the population standard deviation is unknown, the T-test is preferable. If it is known and the sample size is large, then the Z-test is more appropriate.
Use t-tests when dealing with small samples or unknown variance, and z-tests when samples are large and variance is known :)
Yes, you're absolutely right!
T-tests are used when: The sample size is small (n < 30) The population variance is unknown
Z-tests are used when: The sample size is large (n ≥ 30) The population variance is known
If the variance is unknown, it's generally safer to use a t-test for small samples and a z-test for large samples.
Not really,
You should choose the test based on the conditions mentioned above. Applying both tests might give similar results for large samples but could lead to incorrect conclusions for small samples. Ammar Kuti Nasser
- Badges
- Science topic