A proponent of a new proposition on a ballot wants to know whether the proposition is likely to pass. The proposition will pass if it gets more than 50% of the votes. Suppose a poll is taken, and 575 out of 1000 randomly selected people support the proposition. Should the proponent use a hypothesis test or a confidence interval to answer this question? Explain. If it is a hypothesis test, state the hypotheses and find the test statistic, p-value, and conclusion. Use a 1% significance level. If a confidence interval is appropriate, find the approximate 98% confidence interval. In both cases, assume that the necessary conditions have been met. Should the proponent use a hypothesis test or a confidence interval? A. The proponent should use a hypothesis test because the proponent wants to know whether or not the proposition will pass. The proponent should use a confidence interval because the proponent wants to know the proportion of the population who will vote for the proposition. B. OC. The proponent should use a hypothesis test because the proponent wants to know the proportion of the population who will vote for the proposition. OD. Neither is appropriate. If a hypothesis test is the most appropriate approach, determine the null and alternative hypotheses for the hypothesis test. Let p denote the population proportion of voters in favor of the proposition. Select the correct choice below and, if necessary, fill in the answer boxes within your choice. (Type integers or decimals. Do not round.) A. Ho: p= 0.50 Ha:p> 0.50 OC. Ho: p< Ha:p> E. Ho:p> Ha: p< B. Ho: p= Ha: p< D. Ho: p= Ha:p # F. A hypothesis test is not the most appropriate approach. The proponent should use a confidence interval.

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A? Z. 

Find the test statistic for the hypothesis test. Select the correct choice below and, if necessary, fill in the answer box within your choice.

- A. \( z = \) [box]  
  (Round to two decimal places as needed.)

- B. A hypothesis test is not the most appropriate approach. The proponent should use a confidence interval.
Transcribed Image Text:Find the test statistic for the hypothesis test. Select the correct choice below and, if necessary, fill in the answer box within your choice. - A. \( z = \) [box] (Round to two decimal places as needed.) - B. A hypothesis test is not the most appropriate approach. The proponent should use a confidence interval.
**Understanding Hypothesis Testing and Confidence Intervals for Proposition Polling**

A proponent of a new proposition on a ballot is interested in understanding whether the proposition is likely to pass, which requires more than 50% of votes. A poll reveals that 575 out of 1000 randomly selected people support the proposition. The question arises: Should a hypothesis test or a confidence interval be used to address this query? Below are some guidelines and steps to consider.

**Question: Should the proponent use a hypothesis test or a confidence interval?**

- **Option A (Correct):** The proponent should use a hypothesis test because they want to determine if the proposition will pass.
- **Option B:** The proponent should use a confidence interval to know the proportion of the population who will vote for the proposition.
- **Option C:** A hypothesis test is suggested to know the proportion of the population who will vote for the proposition.
- **Option D:** Neither is appropriate.

**Decision:**

- A hypothesis test is most appropriate here because it directly tests whether the proportion of votes is greater than 50%.

**Approach: Hypothesis Test**

Given that a hypothesis test is appropriate, the next step is to determine the null and alternative hypotheses. Let \( p \) denote the population proportion of voters in favor of the proposal. The options for hypothesis statements are:

- **Option A (Correct):**
  - \( H_0: p = 0.50 \) (Null Hypothesis)
  - \( H_a: p > 0.50 \) (Alternative Hypothesis)

- **Option C:** \( H_0: p < \), \( H_a: p > \)
- **Option E:** \( H_0: p > \), \( H_a: p < \)
- **Option B:** \( H_0: p = \), \( H_a: p < \)
- **Option D:** \( H_0: p = \), \( H_a: p \neq \)
- **Option F:** Suggests using a confidence interval instead.

**Conclusion:**

We choose Option A for the hypothesis test to determine if the proportion of those in favor is significantly greater than 50%. This decision aids in evaluating the likelihood of the proposition passing based on the sample results, with a 1% significance level.
Transcribed Image Text:**Understanding Hypothesis Testing and Confidence Intervals for Proposition Polling** A proponent of a new proposition on a ballot is interested in understanding whether the proposition is likely to pass, which requires more than 50% of votes. A poll reveals that 575 out of 1000 randomly selected people support the proposition. The question arises: Should a hypothesis test or a confidence interval be used to address this query? Below are some guidelines and steps to consider. **Question: Should the proponent use a hypothesis test or a confidence interval?** - **Option A (Correct):** The proponent should use a hypothesis test because they want to determine if the proposition will pass. - **Option B:** The proponent should use a confidence interval to know the proportion of the population who will vote for the proposition. - **Option C:** A hypothesis test is suggested to know the proportion of the population who will vote for the proposition. - **Option D:** Neither is appropriate. **Decision:** - A hypothesis test is most appropriate here because it directly tests whether the proportion of votes is greater than 50%. **Approach: Hypothesis Test** Given that a hypothesis test is appropriate, the next step is to determine the null and alternative hypotheses. Let \( p \) denote the population proportion of voters in favor of the proposal. The options for hypothesis statements are: - **Option A (Correct):** - \( H_0: p = 0.50 \) (Null Hypothesis) - \( H_a: p > 0.50 \) (Alternative Hypothesis) - **Option C:** \( H_0: p < \), \( H_a: p > \) - **Option E:** \( H_0: p > \), \( H_a: p < \) - **Option B:** \( H_0: p = \), \( H_a: p < \) - **Option D:** \( H_0: p = \), \( H_a: p \neq \) - **Option F:** Suggests using a confidence interval instead. **Conclusion:** We choose Option A for the hypothesis test to determine if the proportion of those in favor is significantly greater than 50%. This decision aids in evaluating the likelihood of the proposition passing based on the sample results, with a 1% significance level.
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