Table of Contents

**What is a T-Test?**

To compare the means of the two groups, a statistical test known as a t-test is used. The t-test can be used to compare the means of two groups that are independent or dependent. The t-test is also known as the student’s t-test because it was developed by William Sealy Gosset, who used the pseudonym student.

To evaluate whether there is a significant difference between the means of the two groups, the t-test is utilized. The t-test is based on the assumption that the two groups are samples from a population that is normally distributed.

The t-test is used to calculate the probability that the difference between the two-group means is due to chance. The t-test is used to test hypotheses about population means. The t-test is used to calculate a p-value. The p-value is the probability that the difference between the two-group means is due to chance.

A strong statistical test that can be used to compare the means of two groups is the t-test. The t-test can be used to compare the means of two groups that are independent or dependent.

**What is a Z-Test?**

A Z-Test is a statistical test used to compare two population means. When the population standard deviation is known and the sample size is large, the Z-Test is employed. The Standard Normal Test is another name for the Z-Test.

The Z-Test is used to test the null hypothesis that the two-population means are equal. The alternative hypothesis is that the two-population means are not equal. The Standard Normal Distribution is the foundation of the Z-Test.

The Z-Test is used to calculate a Z-Score. The number of standard deviations between the sample means and the population mean is the Z-Score. The Z-Score is used to determine whether the sample mean is significantly different from the population mean.

When the population standard deviation is known and the sample size is large, the Z-Test is employed. It is not used when the population standard deviation is unknown or the sample size is small. It is also not used when the population is not Normally distributed.

**Difference Between T-Test and Z-Test**

- T-tests are used when the population variance is unknown, while Z-tests are used when the population variance is known.
- T-tests can be used for both normal and non-normal distributions, while Z-tests can only be used for normal distributions.
- T-tests are used to compare two means, while Z-tests are used to compare a mean to a population mean.
- T-statistics follow a t-distribution, while Z-statistics follow a normal distribution.
- T-tests are used to calculate a confidence interval for a population mean while Z-tests are used to calculate a confidence interval for a population proportion.
- T-tests are used to test hypotheses about the difference between two population means while Z-tests are used to test hypotheses about the difference between two population proportions.

**Comparison Between T-Test and Z-Test**

Parameters of Comparison | T-Test | Z-Test |

Data size | Greater than 30 | Smaller than 30 |

Points | Isn’t related or does not affect another data point | Might be related to each other where the behaviour or value of one point may affect another |

Distribution of Data | It is normally distributed if the data size is greater than 30 (assuming) | Data is not normally distributed |

Selection | Data is randomly selected from a broader population | Data is not randomly selected |

Sample sizes | Used when the sample sizes are small and they should be equal if possible | Used when the sample sizes are large and they are not equal |