Complete parts (a) through (c) below. (a) Determine the critical value(s) for a right-tailed test of a population mean at the a = 0.05 level of significance with 15 degrees of freedom. (b) Determine the critical value(s) for a left-tailed test of a population mean at the a = 0.05 level of significance based on a sample size of n= 10. (c) Determine the critical value(s) for a two-tailed test of a population mean at the a = 0.01 level of significance based on a sample size of n = 11.

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**Statistical Significance Testing**

Complete parts (a) through (c) below:

(a) Determine the critical value(s) for a right-tailed test of a population mean at the α = 0.05 level of significance with 15 degrees of freedom.

(b) Determine the critical value(s) for a left-tailed test of a population mean at the α = 0.05 level of significance based on a sample size of n = 10.

(c) Determine the critical value(s) for a two-tailed test of a population mean at the α = 0.01 level of significance based on a sample size of n = 11.

- Click here to view the t-Distribution Area in Right Tail.

**Input Area:**

(a) t_crit = [dropdown] [input box] (Round to three decimal places as needed.)
Transcribed Image Text:**Statistical Significance Testing** Complete parts (a) through (c) below: (a) Determine the critical value(s) for a right-tailed test of a population mean at the α = 0.05 level of significance with 15 degrees of freedom. (b) Determine the critical value(s) for a left-tailed test of a population mean at the α = 0.05 level of significance based on a sample size of n = 10. (c) Determine the critical value(s) for a two-tailed test of a population mean at the α = 0.01 level of significance based on a sample size of n = 11. - Click here to view the t-Distribution Area in Right Tail. **Input Area:** (a) t_crit = [dropdown] [input box] (Round to three decimal places as needed.)
This is a T-Distribution Table showing the area in the right tail. It is typically used in statistical analyses to determine the critical t-values for different confidence levels and degrees of freedom.

### Structure of the Table:
- **Rows**: Represent the degrees of freedom (df), ranging from 1 to 1000.
- **Columns**: Represent different significance levels corresponding to the area in the right tail:
  - 0.25
  - 0.20
  - 0.15
  - 0.10
  - 0.05
  - 0.025
  - 0.02
  - 0.01
  - 0.005
  - 0.0025
  - 0.001
  - 0.0005

### Explanation:
- As the degrees of freedom increase, the t-values generally decrease, converging towards a normal distribution curve.
- Each cell in the table provides the t-value for the specified degree of freedom and significance level.

### Usage:
The table is integral in hypothesis testing, particularly in t-tests involving small sample sizes:
- **Step 1**: Determine the degrees of freedom for your test.
- **Step 2**: Identify the significance level for your test.
- **Step 3**: Locate the intersection of the respective row and column to find the critical t-value.

This table assists in deciding whether to accept or reject the null hypothesis.
Transcribed Image Text:This is a T-Distribution Table showing the area in the right tail. It is typically used in statistical analyses to determine the critical t-values for different confidence levels and degrees of freedom. ### Structure of the Table: - **Rows**: Represent the degrees of freedom (df), ranging from 1 to 1000. - **Columns**: Represent different significance levels corresponding to the area in the right tail: - 0.25 - 0.20 - 0.15 - 0.10 - 0.05 - 0.025 - 0.02 - 0.01 - 0.005 - 0.0025 - 0.001 - 0.0005 ### Explanation: - As the degrees of freedom increase, the t-values generally decrease, converging towards a normal distribution curve. - Each cell in the table provides the t-value for the specified degree of freedom and significance level. ### Usage: The table is integral in hypothesis testing, particularly in t-tests involving small sample sizes: - **Step 1**: Determine the degrees of freedom for your test. - **Step 2**: Identify the significance level for your test. - **Step 3**: Locate the intersection of the respective row and column to find the critical t-value. This table assists in deciding whether to accept or reject the null hypothesis.
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