According to a polling organization, 24% of adults in a large region consider themselves to be liberal. A survey asked 200 respondents to disclose their political philosophy: Conservative, Liberal, Moderate. Treat the results of the survey as a random sample of adults in this region. Do the survey results suggest the proportion is higher than that reported by the polling organization? Use an a = 0.10 level of significance. E Click the icon to view the survey results. Because npo (1- Po) =D 10; the sample size is V 5% of the population size, and the sample the V satisfied. requirements for testing the hypothesis (Round to one decimal place as needed.) cannot be reasonably assumed to be random, can be reasonably assumed to be random, is given to be random, is given to not be random.

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**Educational Content - Hypothesis Testing Example**

**Scenario:**
According to a polling organization, 24% of adults in a large region consider themselves to be liberal. A survey conducted with 200 respondents asked them to disclose their political philosophy: Conservative, Liberal, or Moderate. The survey results are treated as a random sample of adults in the region. We want to determine if the survey results suggest that the proportion of liberals is higher than the reported 24% by the polling organization. The significance level for this hypothesis test is set at \( \alpha=0.10 \).

**Interactive Components:**
1. **Survey Results Icon:**
   - Users can click the icon to view detailed survey results.

2. **Hypotheses Test Requirements:**
   - **Formula**: \( np_0(1-p_0) \geq 10 \)
   - Users must input the sample size, which represents a percentage of the population (default shown as 5%), and make selections that demonstrate the requirements for testing the hypothesis.

3. **Drop-down Options:**
   - Options available relate to assumptions and criteria for performing the hypothesis test:
     - “cannot be reasonably assumed to be random”
     - “can be reasonably assumed to be random”
     - “is given to be random”
     - “is given to not be random”

**Instructions:**
- Choose appropriate values and select the correct assumptions to determine whether the sample data satisfies the necessary requirements for performing hypothesis testing in this context.
- Round calculated values to one decimal place as needed.

**Note:** This exercise is designed to improve understanding of hypothesis testing mechanics, specifically in the context of verifying random sample assumptions and sample size requirements when comparing proportions.
Transcribed Image Text:**Educational Content - Hypothesis Testing Example** **Scenario:** According to a polling organization, 24% of adults in a large region consider themselves to be liberal. A survey conducted with 200 respondents asked them to disclose their political philosophy: Conservative, Liberal, or Moderate. The survey results are treated as a random sample of adults in the region. We want to determine if the survey results suggest that the proportion of liberals is higher than the reported 24% by the polling organization. The significance level for this hypothesis test is set at \( \alpha=0.10 \). **Interactive Components:** 1. **Survey Results Icon:** - Users can click the icon to view detailed survey results. 2. **Hypotheses Test Requirements:** - **Formula**: \( np_0(1-p_0) \geq 10 \) - Users must input the sample size, which represents a percentage of the population (default shown as 5%), and make selections that demonstrate the requirements for testing the hypothesis. 3. **Drop-down Options:** - Options available relate to assumptions and criteria for performing the hypothesis test: - “cannot be reasonably assumed to be random” - “can be reasonably assumed to be random” - “is given to be random” - “is given to not be random” **Instructions:** - Choose appropriate values and select the correct assumptions to determine whether the sample data satisfies the necessary requirements for performing hypothesis testing in this context. - Round calculated values to one decimal place as needed. **Note:** This exercise is designed to improve understanding of hypothesis testing mechanics, specifically in the context of verifying random sample assumptions and sample size requirements when comparing proportions.
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