Use software or Table C to find the critical value t∗ corresponding to the middle 98% of the t(21) distribution. the critical value t∗ with area 0.025 to the right of t∗ under the t(24) distribution. the area under the t(5) distribution to the right of t=3.

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Use software or Table C to find

  1. the critical value t∗ corresponding to the middle 98% of the t(21) distribution.
  2. the critical value t∗ with area 0.025 to the right of t∗ under the t(24) distribution.
  3. the area under the t(5) distribution to the right of t=3.
**Table C: t Distribution Critical Values**

The table above provides critical values for the t distribution based on degrees of freedom and confidence levels. It is a reference tool commonly used in statistics for hypothesis testing and constructing confidence intervals.

- **Degrees of Freedom (df):** Listed vertically on the left side of the table, ranging from 1 to 1000.
  
- **Confidence Level (C):** Listed horizontally across the top, ranging from 50% to 99.9%.

For each combination of degrees of freedom and confidence level, the table provides the corresponding critical t value. These values can be used to determine the critical regions in statistical hypothesis testing.

For example, if you have 10 degrees of freedom and are looking for a 95% confidence level, the critical t value is 2.228.

**Graph Explanation:**

- The graph illustrates a t distribution curve.
- The area under the curve represents the probability distribution.
- The shaded region (orange) indicates the probability (p) related to the critical t value (χ*).
- The critical value χ* marks the boundary of this shaded region, separating the tail(s) of the curve where the probability of observing a value as extreme as or more extreme than χ* lies.

This graphical representation helps in visualizing how much of the distribution lies beyond the critical t value, aiding in understanding the concept of significance in hypothesis testing.
Transcribed Image Text:**Table C: t Distribution Critical Values** The table above provides critical values for the t distribution based on degrees of freedom and confidence levels. It is a reference tool commonly used in statistics for hypothesis testing and constructing confidence intervals. - **Degrees of Freedom (df):** Listed vertically on the left side of the table, ranging from 1 to 1000. - **Confidence Level (C):** Listed horizontally across the top, ranging from 50% to 99.9%. For each combination of degrees of freedom and confidence level, the table provides the corresponding critical t value. These values can be used to determine the critical regions in statistical hypothesis testing. For example, if you have 10 degrees of freedom and are looking for a 95% confidence level, the critical t value is 2.228. **Graph Explanation:** - The graph illustrates a t distribution curve. - The area under the curve represents the probability distribution. - The shaded region (orange) indicates the probability (p) related to the critical t value (χ*). - The critical value χ* marks the boundary of this shaded region, separating the tail(s) of the curve where the probability of observing a value as extreme as or more extreme than χ* lies. This graphical representation helps in visualizing how much of the distribution lies beyond the critical t value, aiding in understanding the concept of significance in hypothesis testing.
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