Use the Student's t distribution to find tc for a 0.95 confidence level when the sample is 20. (Round your answer to three decimal places.) Use the Student's t distribution to find tc for a 0.99 confidence level when the sample is 13. Student's t distributions are symmetric about a value of t. What is that t value?

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Use the Student's t distribution to find tc for a 0.95 confidence level when the sample is 20. (Round your answer to three decimal places.)

Use the Student's t distribution to find tc for a 0.99 confidence level when the sample is 13.

Student's t distributions are symmetric about a value of t. What is that t value?

**Critical Values for Student's t Distribution**

**Table 4: Critical Values for Student's t Distribution**

This table provides critical values of the t-distribution for different degrees of freedom (df). The values correspond to various levels of significance (α) for one-tail and two-tail tests. Each column represents a specific significance level for a one-tail test, divided as follows:

- Two-tail area: 0.250, 0.125, 0.100, 0.050, 0.025, 0.020, 0.010, 0.005, 0.002, 0.001
- One-tail area: 0.500, 0.250, 0.200, 0.100, 0.050, 0.040, 0.020, 0.010, 0.004, 0.002

**Degrees of Freedom (df)**
- A range of df values is listed, from 1 to 100.

**Graphics Explanation**

1. The first diagram shows a **two-tail area**. It illustrates the t-distribution curve with two shaded regions in the tails, representing the rejection regions for a two-tail test.

2. The second diagram illustrates a **left-tail area**. This diagram shows the left tail of the distribution shaded, indicative of a one-tail test focused on values less than the mean.

3. The third diagram represents a **right-tail area**. It shows the right tail of the distribution shaded, used for one-tail tests for values greater than the mean.

**Instructions:**
For a given df not found in the table, use linear interpolation to estimate the critical value.

This table is essential for statistical analysis when conducting hypothesis testing and determining confidence intervals using the t-distribution.
Transcribed Image Text:**Critical Values for Student's t Distribution** **Table 4: Critical Values for Student's t Distribution** This table provides critical values of the t-distribution for different degrees of freedom (df). The values correspond to various levels of significance (α) for one-tail and two-tail tests. Each column represents a specific significance level for a one-tail test, divided as follows: - Two-tail area: 0.250, 0.125, 0.100, 0.050, 0.025, 0.020, 0.010, 0.005, 0.002, 0.001 - One-tail area: 0.500, 0.250, 0.200, 0.100, 0.050, 0.040, 0.020, 0.010, 0.004, 0.002 **Degrees of Freedom (df)** - A range of df values is listed, from 1 to 100. **Graphics Explanation** 1. The first diagram shows a **two-tail area**. It illustrates the t-distribution curve with two shaded regions in the tails, representing the rejection regions for a two-tail test. 2. The second diagram illustrates a **left-tail area**. This diagram shows the left tail of the distribution shaded, indicative of a one-tail test focused on values less than the mean. 3. The third diagram represents a **right-tail area**. It shows the right tail of the distribution shaded, used for one-tail tests for values greater than the mean. **Instructions:** For a given df not found in the table, use linear interpolation to estimate the critical value. This table is essential for statistical analysis when conducting hypothesis testing and determining confidence intervals using the t-distribution.
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