Find the t value(s) for each of the following cases. (Round your answers to three decimal places.) (a) upper tail area of 0.025 with 16 degrees of freedom (b) lower tail area of 0.05 with 54 degrees of freedom (c) upper tail area of 0.01 with 32 degrees of freedom

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**Finding the t Value(s) for Specific Cases**

Use the following instructions to find the t value(s) for each scenario provided. Make sure to round your answers to three decimal places.

1. **Case (a)**
   - *Description*: Determine the t value for an upper tail area of 0.025 with 16 degrees of freedom.
   - *Input Box*: ___________________

2. **Case (b)**
   - *Description*: Find the t value for a lower tail area of 0.05 with 54 degrees of freedom.
   - *Input Box*: ___________________

3. **Case (c)**
   - *Description*: Calculate the t value for an upper tail area of 0.01 with 32 degrees of freedom.
   - *Input Box*: ___________________

4. **Case (d)**
   - *Description*: Identify two t values such that 90% of the area falls between these values, with 29 degrees of freedom. Both t values should be equidistant from zero.
   - *Smaller Value Input*: ___________________
   - *Larger Value Input*: ___________________

5. **Case (e)**
   - *Description*: Find the two t values where 95% of the area falls between them, with 45 degrees of freedom. Both t values should be equidistant from zero.
   - *Smaller Value Input*: ___________________
   - *Larger Value Input*: ___________________

This practice helps in understanding the use of t-distributions in statistical analysis, particularly in hypothesis testing and confidence interval estimation.
Transcribed Image Text:**Finding the t Value(s) for Specific Cases** Use the following instructions to find the t value(s) for each scenario provided. Make sure to round your answers to three decimal places. 1. **Case (a)** - *Description*: Determine the t value for an upper tail area of 0.025 with 16 degrees of freedom. - *Input Box*: ___________________ 2. **Case (b)** - *Description*: Find the t value for a lower tail area of 0.05 with 54 degrees of freedom. - *Input Box*: ___________________ 3. **Case (c)** - *Description*: Calculate the t value for an upper tail area of 0.01 with 32 degrees of freedom. - *Input Box*: ___________________ 4. **Case (d)** - *Description*: Identify two t values such that 90% of the area falls between these values, with 29 degrees of freedom. Both t values should be equidistant from zero. - *Smaller Value Input*: ___________________ - *Larger Value Input*: ___________________ 5. **Case (e)** - *Description*: Find the two t values where 95% of the area falls between them, with 45 degrees of freedom. Both t values should be equidistant from zero. - *Smaller Value Input*: ___________________ - *Larger Value Input*: ___________________ This practice helps in understanding the use of t-distributions in statistical analysis, particularly in hypothesis testing and confidence interval estimation.
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