A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Question
Answer all A, B, C questions
**P-Value for Hypothesis Testing** The P-value for a hypothesis test is shown. Use the P-value to decide whether to reject \( H_0 \) when the level of significance is (a) \( \alpha = 0.01 \), (b) \( \alpha = 0.05 \), and (c) \( \alpha = 0.10 \). **P = 0.0308** --- **(a) Do you reject or fail to reject \( H_0 \) at the 0.01 level of significance?** - **A.** Reject \( H_0 \) because the P-value, 0.0308, is greater than \( \alpha = 0.01 \). - **B.** Fail to reject \( H_0 \) because the P-value, 0.0308, is less than \( \alpha = 0.01 \). - **C.** Reject \( H_0 \) because the P-value, 0.0308, is less than \( \alpha = 0.01 \). - **D.** Fail to reject \( H_0 \) because the P-value, 0.0308, is greater than \( \alpha = 0.01 \). --- **(b) Do you reject or fail to reject \( H_0 \) at the 0.05 level of significance?** - **A.** Reject \( H_0 \) because the P-value, 0.0308, is less than \( \alpha = 0.05 \). - **B.** Fail to reject \( H_0 \) because the P-value, 0.0308, is less than \( \alpha = 0.05 \). - **C.** Fail to reject \( H_0 \) because the P-value, 0.0308, is greater than \( \alpha = 0.05 \). - **D.** Reject \( H_0 \) because the P-value, 0.0308, is greater than \( \alpha = 0.05 \). --- **Note:** The "Next" button is provided at the bottom right of the page but is not functional as this is a screenshot.
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Transcribed Image Text:**P-Value for Hypothesis Testing** The P-value for a hypothesis test is shown. Use the P-value to decide whether to reject \( H_0 \) when the level of significance is (a) \( \alpha = 0.01 \), (b) \( \alpha = 0.05 \), and (c) \( \alpha = 0.10 \). **P = 0.0308** --- **(a) Do you reject or fail to reject \( H_0 \) at the 0.01 level of significance?** - **A.** Reject \( H_0 \) because the P-value, 0.0308, is greater than \( \alpha = 0.01 \). - **B.** Fail to reject \( H_0 \) because the P-value, 0.0308, is less than \( \alpha = 0.01 \). - **C.** Reject \( H_0 \) because the P-value, 0.0308, is less than \( \alpha = 0.01 \). - **D.** Fail to reject \( H_0 \) because the P-value, 0.0308, is greater than \( \alpha = 0.01 \). --- **(b) Do you reject or fail to reject \( H_0 \) at the 0.05 level of significance?** - **A.** Reject \( H_0 \) because the P-value, 0.0308, is less than \( \alpha = 0.05 \). - **B.** Fail to reject \( H_0 \) because the P-value, 0.0308, is less than \( \alpha = 0.05 \). - **C.** Fail to reject \( H_0 \) because the P-value, 0.0308, is greater than \( \alpha = 0.05 \). - **D.** Reject \( H_0 \) because the P-value, 0.0308, is greater than \( \alpha = 0.05 \). --- **Note:** The "Next" button is provided at the bottom right of the page but is not functional as this is a screenshot.
The image contains a prompt related to hypothesis testing, specifically involving decisions based on P-values and significance levels: --- **P-value for a Hypothesis Test:** Use the P-value to decide whether to reject \( H_0 \) (the null hypothesis) when the level of significance is: - (a) \( \alpha = 0.01 \) - (b) \( \alpha = 0.05 \) - (c) \( \alpha = 0.10 \) **Given:** \[ P = 0.0308 \] **Options for decision making:** 1. **For \( \alpha = 0.05 \):** - **A.** Reject \( H_0 \) because the P-value, 0.0308, is less than \( \alpha = 0.05 \). - **B.** Fail to reject \( H_0 \) because the P-value, 0.0308, is less than \( \alpha = 0.05 \). - **C.** Fail to reject \( H_0 \) because the P-value, 0.0308, is greater than \( \alpha = 0.05 \). - **D.** Reject \( H_0 \) because the P-value, 0.0308, is greater than \( \alpha = 0.05 \). 2. **For \( \alpha = 0.10 \):** - **A.** Reject \( H_0 \) because the P-value, 0.0308, is less than \( \alpha = 0.10 \). - **B.** Fail to reject \( H_0 \) because the P-value, 0.0308, is less than \( \alpha = 0.10 \). - **C.** Fail to reject \( H_0 \) because the P-value, 0.0308, is greater than \( \alpha = 0.10 \). - **D.** Reject \( H_0 \) because the P-value, 0.0308, is greater than \( \alpha = 0.10 \). --- There are no graphs or diagrams present in the image.
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Transcribed Image Text:The image contains a prompt related to hypothesis testing, specifically involving decisions based on P-values and significance levels: --- **P-value for a Hypothesis Test:** Use the P-value to decide whether to reject \( H_0 \) (the null hypothesis) when the level of significance is: - (a) \( \alpha = 0.01 \) - (b) \( \alpha = 0.05 \) - (c) \( \alpha = 0.10 \) **Given:** \[ P = 0.0308 \] **Options for decision making:** 1. **For \( \alpha = 0.05 \):** - **A.** Reject \( H_0 \) because the P-value, 0.0308, is less than \( \alpha = 0.05 \). - **B.** Fail to reject \( H_0 \) because the P-value, 0.0308, is less than \( \alpha = 0.05 \). - **C.** Fail to reject \( H_0 \) because the P-value, 0.0308, is greater than \( \alpha = 0.05 \). - **D.** Reject \( H_0 \) because the P-value, 0.0308, is greater than \( \alpha = 0.05 \). 2. **For \( \alpha = 0.10 \):** - **A.** Reject \( H_0 \) because the P-value, 0.0308, is less than \( \alpha = 0.10 \). - **B.** Fail to reject \( H_0 \) because the P-value, 0.0308, is less than \( \alpha = 0.10 \). - **C.** Fail to reject \( H_0 \) because the P-value, 0.0308, is greater than \( \alpha = 0.10 \). - **D.** Reject \( H_0 \) because the P-value, 0.0308, is greater than \( \alpha = 0.10 \). --- There are no graphs or diagrams present in the image.
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We have to decide if we reject H0 or not for given level of confidence and p value.

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