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Find the critical value(s) and rejection region(s) for the indicated t-test, level of significance a, and sample size n. Right-tailed test, a= 0.05, n= 10 Click the icon to view the t-distribution table. ..... The critical value(s) is/are. (Round to the nearest thousandth as needed. Use a comma to separate answers as needed.)

Find the critical value(s) and rejection region(s) for the indicated t-test, level of significance a, and sample size n. Right-tailed test, a= 0.05, n= 10 Click the icon to view the t-distribution table. ..... The critical value(s) is/are. (Round to the nearest thousandth as needed. Use a comma to separate answers as needed.)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Find the critical value and rejection region
**Transcription and Explanation for Educational Website** **Task Description:** Find the critical value(s) and rejection region(s) for the indicated t-test, level of significance α, and sample size n. - **Right-tailed test, α = 0.05, n = 10** - Click the icon to view the t-distribution table. --- **Critical Value Calculation:** The critical value(s) is/are [ ] (Round to the nearest thousandth as needed. Use a comma to separate answers as needed.) --- **Instructions:** 1. **Identify the Type of Test:** - This is a right-tailed test which indicates we are looking for the critical value in the upper tail of the t-distribution. 2. **Level of Significance (α):** - The level of significance is 0.05. This is used to determine the threshold at which we will reject the null hypothesis. 3. **Sample Size (n):** - The sample size is 10, which implies 9 degrees of freedom (n-1). 4. **Finding the t-Distribution Value:** - You can find the critical value by referring to a t-distribution table or using statistical software. Look for t0.05 with 9 degrees of freedom in the table. 5. **Round the Critical Value:** - Ensure to round the result to the nearest thousandth, as specified. 6. **Determine Rejection Region:** - Based on the critical value, you will determine the rejection region where, if the test statistic falls, the null hypothesis is rejected. **Note:** No graphs or diagrams are provided in the original text. The user is prompted to view a t-distribution table, which should be accessed separately to find the critical value needed for this calculation.
Transcribed Image Text:**Transcription and Explanation for Educational Website** **Task Description:** Find the critical value(s) and rejection region(s) for the indicated t-test, level of significance α, and sample size n. - **Right-tailed test, α = 0.05, n = 10** - Click the icon to view the t-distribution table. --- **Critical Value Calculation:** The critical value(s) is/are [ ] (Round to the nearest thousandth as needed. Use a comma to separate answers as needed.) --- **Instructions:** 1. **Identify the Type of Test:** - This is a right-tailed test which indicates we are looking for the critical value in the upper tail of the t-distribution. 2. **Level of Significance (α):** - The level of significance is 0.05. This is used to determine the threshold at which we will reject the null hypothesis. 3. **Sample Size (n):** - The sample size is 10, which implies 9 degrees of freedom (n-1). 4. **Finding the t-Distribution Value:** - You can find the critical value by referring to a t-distribution table or using statistical software. Look for t0.05 with 9 degrees of freedom in the table. 5. **Round the Critical Value:** - Ensure to round the result to the nearest thousandth, as specified. 6. **Determine Rejection Region:** - Based on the critical value, you will determine the rejection region where, if the test statistic falls, the null hypothesis is rejected. **Note:** No graphs or diagrams are provided in the original text. The user is prompted to view a t-distribution table, which should be accessed separately to find the critical value needed for this calculation.
### T-Distribution Table Explanation The image depicts a portion of a statistical t-distribution table, which is used to find critical values for t-tests. The table helps in determining the rejection regions for hypothesis testing. #### Components of the T-Distribution Table: - **Degrees of Freedom (d.f.):** This is represented in the first column. It ranges from 1 to 17 in this segment of the table. - **Levels of Significance (α) and Confidence Levels (c):** At the top of the table are the confidence levels and corresponding α values: - Confidence levels are displayed as 0.80, 0.90, 0.95, 0.98, and 0.99. - The associated alpha values are 0.10, 0.05, 0.025, 0.01, and 0.005. - **Rows and Columns:** - Each row corresponds to a different degree of freedom. - Each column under the confidence levels provides the critical t-value for that level of confidence and degree of freedom. #### Example Reading: For a degree of freedom (d.f.) of 5: - At a confidence level of 0.95 (α = 0.05), the critical t-value is 2.571. This table is used in statistical hypothesis testing to determine whether to reject the null hypothesis. Ensure the degrees of freedom and desired confidence level are known to select the accurate critical value. ### Use in Educational Context When interpreting this table in an educational setting, students typically use it in courses involving statistics, such as psychology, biology, and economics, where it's important to understand variability in data sets with smaller sample sizes. The t-distribution is particularly useful when the sample size is too small to assume a normal distribution of the population data.
Transcribed Image Text:### T-Distribution Table Explanation The image depicts a portion of a statistical t-distribution table, which is used to find critical values for t-tests. The table helps in determining the rejection regions for hypothesis testing. #### Components of the T-Distribution Table: - **Degrees of Freedom (d.f.):** This is represented in the first column. It ranges from 1 to 17 in this segment of the table. - **Levels of Significance (α) and Confidence Levels (c):** At the top of the table are the confidence levels and corresponding α values: - Confidence levels are displayed as 0.80, 0.90, 0.95, 0.98, and 0.99. - The associated alpha values are 0.10, 0.05, 0.025, 0.01, and 0.005. - **Rows and Columns:** - Each row corresponds to a different degree of freedom. - Each column under the confidence levels provides the critical t-value for that level of confidence and degree of freedom. #### Example Reading: For a degree of freedom (d.f.) of 5: - At a confidence level of 0.95 (α = 0.05), the critical t-value is 2.571. This table is used in statistical hypothesis testing to determine whether to reject the null hypothesis. Ensure the degrees of freedom and desired confidence level are known to select the accurate critical value. ### Use in Educational Context When interpreting this table in an educational setting, students typically use it in courses involving statistics, such as psychology, biology, and economics, where it's important to understand variability in data sets with smaller sample sizes. The t-distribution is particularly useful when the sample size is too small to assume a normal distribution of the population data.
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