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,
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Chapter1: Combinatorial Analysis
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Answer these question A, B, C and D questions

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.

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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