Use the Student's t-distribution to find the t-value for each of the given scenarios. Round t-values to four decimal places. • Find the value of t such that the area in the left tail of the t-distribution is 0.025, if the sample size is 47. t = • Find the value of t such that the area in the right tail of the t-distribution is 0.1, if the sample size is 95. t = • Find the value of t such that the area in the left tail of the t-distribution is 0.05, if the sample size is 112. t=

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Author:Carter
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Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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### Utilizing the Student's t-Distribution to Calculate t-Values

In this section, we will use the Student's t-distribution to find specific t-values for given scenarios. Ensure to round your t-values to four decimal places as required.

1. **Given Scenario:**
   - **Condition:** The area in the left tail of the t-distribution is 0.025.
   - **Sample Size:** 47.
   - **Instruction:** Find the t-value.
   
   \[
   t = \_\_\_\_
   \]

2. **Given Scenario:**
   - **Condition:** The area in the right tail of the t-distribution is 0.1.
   - **Sample Size:** 95.
   - **Instruction:** Find the t-value.
   
   \[
   t = \_\_\_\_
   \]

3. **Given Scenario:**
   - **Condition:** The area in the left tail of the t-distribution is 0.05.
   - **Sample Size:** 112.
   - **Instruction:** Find the t-value.
   
   \[
   t = \_\_\_\_
   \]

4. **Given Scenario:**
   - **Condition:** 95% of the area under the t-distribution is centered around the mean.
   - **Sample Size:** 86.
   - **Instruction:** Find the two t-values and enter the solutions using a comma-separated list.
   
   \[
   t = \_\_\_\_, \_\_\_\_
   \]

Use the appropriate t-distribution tables or statistical software to find the required t-values. Input these values to complete the tasks accurately. This exercise is critical in understanding how to apply the t-distribution in various statistical analyses.
Transcribed Image Text:### Utilizing the Student's t-Distribution to Calculate t-Values In this section, we will use the Student's t-distribution to find specific t-values for given scenarios. Ensure to round your t-values to four decimal places as required. 1. **Given Scenario:** - **Condition:** The area in the left tail of the t-distribution is 0.025. - **Sample Size:** 47. - **Instruction:** Find the t-value. \[ t = \_\_\_\_ \] 2. **Given Scenario:** - **Condition:** The area in the right tail of the t-distribution is 0.1. - **Sample Size:** 95. - **Instruction:** Find the t-value. \[ t = \_\_\_\_ \] 3. **Given Scenario:** - **Condition:** The area in the left tail of the t-distribution is 0.05. - **Sample Size:** 112. - **Instruction:** Find the t-value. \[ t = \_\_\_\_ \] 4. **Given Scenario:** - **Condition:** 95% of the area under the t-distribution is centered around the mean. - **Sample Size:** 86. - **Instruction:** Find the two t-values and enter the solutions using a comma-separated list. \[ t = \_\_\_\_, \_\_\_\_ \] Use the appropriate t-distribution tables or statistical software to find the required t-values. Input these values to complete the tasks accurately. This exercise is critical in understanding how to apply the t-distribution in various statistical analyses.
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