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State whether the standardized test staustic t indicates that you should reject the null hypotnesis. Explain. (a) t= 1.932 (b) t=0 (c) t= 1.801 (d) t= - 1.905 to1.805 .... (a) For t= 1.932, should you reject or fail to reject the null hypothesis? O A. Fail to reject Ho, because t> 1.895. O B. Fail to reject Ho, because t<1.895. O C. Reject Ho, because t> 1.895,

State whether the standardized test staustic t indicates that you should reject the null hypotnesis. Explain. (a) t= 1.932 (b) t=0 (c) t= 1.801 (d) t= - 1.905 to1.805 .... (a) For t= 1.932, should you reject or fail to reject the null hypothesis? O A. Fail to reject Ho, because t> 1.895. O B. Fail to reject Ho, because t<1.895. O C. Reject Ho, because t> 1.895,

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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**Transcription and Explanation for Educational Use:** **Title: Hypothesis Testing with Standardized Test Statistics** State whether the standardized test statistic \( t \) indicates that you should reject the null hypothesis. Explain: (a) \( t = 1.932 \) (b) \( t = 0 \) (c) \( t = 1.801 \) (d) \( t = -1.905 \) **Question (a):** For \( t = 1.932 \), should you reject or fail to reject the null hypothesis? - **A.** Fail to reject \( H_0 \), because \( t > 1.895 \). - **B.** Fail to reject \( H_0 \), because \( t < 1.895 \). - **C.** Reject \( H_0 \), because \( t > 1.895 \). - **D.** Reject \( H_0 \), because \( t < 1.895 \). **Question (b):** For \( t = 0 \), should you reject or fail to reject the null hypothesis? - **A.** Fail to reject \( H_0 \), because \( t > 1.895 \). - **B.** Fail to reject \( H_0 \), because \( t < 1.895 \). - **C.** Reject \( H_0 \), because \( t > 1.895 \). - **D.** Reject \( H_0 \), because \( t < 1.895 \). **Diagram Explanation:** - The image includes a bell-shaped curve, representing the distribution of the test statistic under the null hypothesis. - The critical value \( t_c = 1.895 \) is marked on the x-axis. - The area to the right of \( t = 1.895 \) is shaded, indicating the rejection region. **Utilities Displayed:** - **Statcrunch**: A tool for statistical analysis. - **Calculator**: A digital tool for calculations. This setup helps in understanding how to interpret the t-statistic in determining whether to reject or fail to reject the null hypothesis based on its comparison to the critical value.
Transcribed Image Text:**Transcription and Explanation for Educational Use:** **Title: Hypothesis Testing with Standardized Test Statistics** State whether the standardized test statistic \( t \) indicates that you should reject the null hypothesis. Explain: (a) \( t = 1.932 \) (b) \( t = 0 \) (c) \( t = 1.801 \) (d) \( t = -1.905 \) **Question (a):** For \( t = 1.932 \), should you reject or fail to reject the null hypothesis? - **A.** Fail to reject \( H_0 \), because \( t > 1.895 \). - **B.** Fail to reject \( H_0 \), because \( t < 1.895 \). - **C.** Reject \( H_0 \), because \( t > 1.895 \). - **D.** Reject \( H_0 \), because \( t < 1.895 \). **Question (b):** For \( t = 0 \), should you reject or fail to reject the null hypothesis? - **A.** Fail to reject \( H_0 \), because \( t > 1.895 \). - **B.** Fail to reject \( H_0 \), because \( t < 1.895 \). - **C.** Reject \( H_0 \), because \( t > 1.895 \). - **D.** Reject \( H_0 \), because \( t < 1.895 \). **Diagram Explanation:** - The image includes a bell-shaped curve, representing the distribution of the test statistic under the null hypothesis. - The critical value \( t_c = 1.895 \) is marked on the x-axis. - The area to the right of \( t = 1.895 \) is shaded, indicating the rejection region. **Utilities Displayed:** - **Statcrunch**: A tool for statistical analysis. - **Calculator**: A digital tool for calculations. This setup helps in understanding how to interpret the t-statistic in determining whether to reject or fail to reject the null hypothesis based on its comparison to the critical value.
The image presents a statistical problem involving hypothesis testing. Students are asked to determine whether the standardized test statistic \( t \) indicates that they should reject the null hypothesis. They are given several values for \( t \) and must use these to make their decision based on a critical value of \( t = 1.895 \). **Given Values and Options:** 1. (a) \( t = 1.932 \) 2. (b) \( t = 1.801 \) 3. (c) \( t = 1.905 \) 4. (d) \( t = -1.905 \) **Questions:** - (a)–(c): Decide if each scenario should reject the null hypothesis based on the criteria \( t > 1.895 \). - (d): Specifically asks if \( t = -1.905 \) leads to rejecting or failing to reject the null hypothesis. **Multiple Choice Answers:** - **A.** Fail to reject \( H_0 \), because \( t < 1.895 \). - **B.** Reject \( H_0 \), because \( t > 1.895 \). - **C.** Reject \( H_0 \), because \( t < 1.895 \). - **D.** Fail to reject \( H_0 \), because \( t > 1.895 \). **Graph Explanation:** A graph on the right shows a t-distribution curve where a critical region is depicted. The critical value marked is \( t = 1.895 \). The graph visually demonstrates the rejection region for the null hypothesis, with the area beyond \( t = 1.895 \) shaded to indicate where we would reject \( H_0 \). This image and explanation guide students through understanding the decision-making process in hypothesis testing based on calculated t-values and critical thresholds.
Transcribed Image Text:The image presents a statistical problem involving hypothesis testing. Students are asked to determine whether the standardized test statistic \( t \) indicates that they should reject the null hypothesis. They are given several values for \( t \) and must use these to make their decision based on a critical value of \( t = 1.895 \). **Given Values and Options:** 1. (a) \( t = 1.932 \) 2. (b) \( t = 1.801 \) 3. (c) \( t = 1.905 \) 4. (d) \( t = -1.905 \) **Questions:** - (a)–(c): Decide if each scenario should reject the null hypothesis based on the criteria \( t > 1.895 \). - (d): Specifically asks if \( t = -1.905 \) leads to rejecting or failing to reject the null hypothesis. **Multiple Choice Answers:** - **A.** Fail to reject \( H_0 \), because \( t < 1.895 \). - **B.** Reject \( H_0 \), because \( t > 1.895 \). - **C.** Reject \( H_0 \), because \( t < 1.895 \). - **D.** Fail to reject \( H_0 \), because \( t > 1.895 \). **Graph Explanation:** A graph on the right shows a t-distribution curve where a critical region is depicted. The critical value marked is \( t = 1.895 \). The graph visually demonstrates the rejection region for the null hypothesis, with the area beyond \( t = 1.895 \) shaded to indicate where we would reject \( H_0 \). This image and explanation guide students through understanding the decision-making process in hypothesis testing based on calculated t-values and critical thresholds.
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