... # A Quick Summary: t-tests vs. Z-tests **When should you use a t-test?** You should use a t-test when *the sample size $n<30$ and / or the population variance is unknown.* **When should you use a Z-test?** You should use a Z-test when *the sample size is $n\geq30$ and / or the variance is known.* **What distribution should the data have in order to use a t-test or a Z-test?** In order to use a t-test or a Z-test, the data should have *a normal distribution.* # An Introduction to Hypothesis Testing **What are the two complementary statements at the core of hypothesis testing?** At the core of hypothesis testing, the two complementary statements are: 1. The null hypothesis ($H_0$) - There's no effect, difference, or relationship. 2. The alternative hypothesis ($H_1$) - The new understanding that the researcher wants to prove. ... # What is a t-test? **What is a t-test?** A t-test is *a statistical test that determines if there's a significant difference between the means of two groups or between a sample mean and a known value.* **What is the formula for the t-test statistic?** The formula for the t-test statistic is: $t=\dfrac{\overline X-\mu}{s/\sqrt n}$ > **What are the variables for the t-test statistic?** > The variables for the t-test statistic are: > * $\overline X$ - The sample mean. > * $\mu$ - The population mean. > * $s$ - The sample standard deviation. > * $n$ - The sample size. # Types of t-tests **What are the three types of t-tests and what they compare?** The three types of t-tests are: 1. One-sample t-test - Compares the mean of a single sample to a known value or population mean. 2. Independent two-sample t-test - Compares the means of two independent groups to determine if there is a statistically significant difference between them. 3. Paired t-test - Compares the means from the same group at different times or under different conditions. # Assumptions of the t-test **What are the three assumptions a t-test relies on to provide valid results?** The three assumptions a t-test relies on to provide valid results are: 1. Normality of the data. 2. Homogeneity of variances. 3. Independence of observations. # What is a Z-test? A Z-test is *a statistical test that determines if there's a significant difference between the sample mean and the population mean or between the means of two groups when the population variance is known, and the sample size is large.* **What is the formula for the Z-test statistic?** The formula for the Z-test statistic is: $z=\dfrac{\overline X-\mu}{\sigma/\sqrt n}$ > **What are the variables for the Z-test statistic?** > The variables for the Z-test statistic are: > * $\overline X$ - The sample mean. > * $\mu$ - The population mean. > * $\sigma$ - The population standard deviation. > * $n$ - The sample size. # Types of Z-tests **What are the three types of Z-tests and what they compare?** The three types of Z-tests and what they compare are: 1. One-sample Z-test - Compares the mean of a single sample to a known population mean. 2. Two-sample Z-test - Compares the means of two independent samples to determine if there's a significant difference between them. 3. Proportion Z-test - Compares the proportion of a certain characteristic in a sample to a known population or between two sample proportions. # Assumptions Of The Z-Test **What are the three assumptions a Z-test relies on to provide valid results?** The three assumptions a Z-test relies on to provide valid results are: 1. Known population variance. 2. Large sample size. 3. Normal distribution of the population. ...