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=
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=
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F090c748e-ae6e-4835-a77f-8d1d8bf06681%2F5ba05def-dc06-474e-95b7-ae5ff98cf47a%2Fv8yydkm_processed.jpeg&w=3840&q=75)
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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