A t-score table is a statistical table that enables you to determine the probability of a particular t-statistic in a t-distribution.

- The t-score table is used when a sample size is too small, and the population standard deviation is unknown.
- It helps in estimating the probability that a sample mean has been drawn from a normal distribution with a specific mean and variance.
- The t-score table is also used in hypothesis testing with a test statistic of the t-distribution.
- The table shows the critical t-value at a given significance level, degrees of freedom, and one-tailed or two-tailed tests.
- The t-score table is generally used for small sample sizes, whereas the z-score table is used for large sample sizes.
- The degrees of freedom represent the number of observations in a sample that can vary independently.
- Using the t-score table, you can determine if the t-value is significant and at what level of significance, e.g., 5%, 1%, or 0.1%.
- The t-score table is based on the Student’s t-distribution, named after the pseudonym William Sealy Gosset, who developed the distribution.
- The table is organized by degrees of freedom and significance level values that show critical values of the t-distribution.

Overall, the t-score table is a valuable tool in statistics that helps in determining the probability of a particular t-statistic given a t-distribution with specific parameters and conditions.

## Example problem for t score table

What is a t score table?

- A t score table is a statistical table that helps calculate the probability of obtaining a certain t statistic in a t-test.
- The t score table contains rows for degrees of freedom (df) and columns for significance levels (α).
- To use the t score table, find the row that corresponds to the degrees of freedom of your sample and the column that corresponds to your chosen level of significance.
- The intersection of the row and column will give you the critical t value for that specific test.

What is the purpose of a t score table?

- The purpose of a t score table is to help determine whether the difference between two sample means is statistically significant or just due to chance.
- We use the t score table to find the critical t value for a given sample size and level of significance, which is then compared to the calculated t value from our sample data.
- If the calculated t value is greater than the critical t value, we can reject the null hypothesis and conclude that there is a statistically significant difference between the sample means.

What are the limitations of a t score table?

- A t score table is only applicable when we are dealing with small sample sizes (typically less than 30).
- If our sample size exceeds 30, we can use a z score table instead.
- It is important to note that a t score table only provides critical values for two-tailed tests. If we are conducting a one-tailed test, we need to adjust our level of significance accordingly.