According to a reputable magazine, 33% of people in a certain large country have sleepwalked at least once in their lives. Suppose a random sample of 250 people showed that 60 reported sleepwalking. Carry out the first two steps of a hypothesis test that will test whether the proportion of people who have sleepwalked is 0.33. Use a significance level of 0.05. Explain how someone would fill in the required entries for Po, x, n, and prop shown in the accompanying figure, where Po is the hypothesized proportion, x is the number of successes, n is the number of observations, and prop is the alternative hypothesis. A Click the icon to view the technology input figure. Determine the null and alternative hypotheses. Họ:p = 0.33 Ha:p * 0.33 (Type integers or decimals. Do not round.) Check the conditions for the one-proportion z-test. Are any conditions not satisfied? Select all that apply. O A. The Random Sample condition is not satisfied cannot be reasonably assumed. O B. The Large Sample Size condition is not satisfied or cannot be reasonably assumed. O c. The Independence condition is not satisfied or cannot be reasonably assumed. O D. The Large Population condition is not satisfied or cannot be reasonably assumed. YE. All conditions are satisfied can be reasonably assumed. Identify the appropriate entries for Po. X, n, and prop in the technology input figure. Po X: n: prop: (Do not round.)

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This image is a snippet from a statistics problem interface, likely related to hypothesis testing involving proportions. 

**Elements in the Image:**

1. **Input Fields:**
   - **p₀ (p sub zero):** A field for entering the null hypothesis proportion.
   - **x:** A field for entering the number of successes in the sample.
   - **n:** A field for entering the sample size.
   
2. **Dropdown Menu:**
   - Contains options for choosing the type of test to perform:
     - "< p₀" (less than p₀)
     - "≠ p₀" (not equal to p₀)
     - "> p₀" (greater than p₀)

3. **Prop (Proportion) Dropdown:**
   - Likely to select a specific proportion for the test.
   
4. **Notation:**
   - "(Do not round.)" indicates that exact values should be used, not approximations.

This form is used to configure and conduct statistical tests on sample data to determine whether the sample proportion differs from a hypothesized population proportion.
Transcribed Image Text:This image is a snippet from a statistics problem interface, likely related to hypothesis testing involving proportions. **Elements in the Image:** 1. **Input Fields:** - **p₀ (p sub zero):** A field for entering the null hypothesis proportion. - **x:** A field for entering the number of successes in the sample. - **n:** A field for entering the sample size. 2. **Dropdown Menu:** - Contains options for choosing the type of test to perform: - "< p₀" (less than p₀) - "≠ p₀" (not equal to p₀) - "> p₀" (greater than p₀) 3. **Prop (Proportion) Dropdown:** - Likely to select a specific proportion for the test. 4. **Notation:** - "(Do not round.)" indicates that exact values should be used, not approximations. This form is used to configure and conduct statistical tests on sample data to determine whether the sample proportion differs from a hypothesized population proportion.
**Hypothesis Testing for Sleepwalking Study**

According to a reputable magazine, 33% of people in a certain large country have sleepwalked at least once in their lives. Suppose a random sample of 250 people showed that 60 reported sleepwalking. We will carry out the first two steps of a hypothesis test to determine if the proportion differs from 0.33, using a significance level of 0.05.

**Step 1: Determine the Null and Alternative Hypotheses**
- Null Hypothesis (H₀): \( p = 0.33 \)
- Alternative Hypothesis (Hₐ): \( p \neq 0.33 \)

(Enter integers or decimals. Do not round.)

**Step 2: Check Conditions for the One-Proportion Z-Test**
Select all the conditions that are not satisfied:
- [ ] A. The Random Sample condition is not satisfied or cannot be reasonably assumed.
- [ ] B. The Large Sample Size condition is not satisfied or cannot be reasonably assumed.
- [ ] C. The Independence condition is not satisfied or cannot be reasonably assumed.
- [x] D. The Large Population condition is not satisfied or cannot be reasonably assumed.
- [ ] E. All conditions are satisfied or can be reasonably assumed.

**Step 3: Identify Entries for Technology Input Figure**
Fill in the values:
- \( p_0 \): \( 0.33 \)
- \( x \): \( 60 \)
- \( n \): \( 250 \)
- \( \text{prop} \): Not to be rounded.

These values are essential inputs for statistical software or calculators used to perform the hypothesis test. The entries correspond to:
- \( p_0 \): Hypothesized proportion
- \( x \): Number of successes (people who reported sleepwalking)
- \( n \): Total number of observations in the sample
- prop: Sample proportion of successes (calculated as \( \frac{x}{n} \))

This educational content serves to guide through the initial steps of hypothesis testing focused on understanding population proportions and assessing statistical significance.
Transcribed Image Text:**Hypothesis Testing for Sleepwalking Study** According to a reputable magazine, 33% of people in a certain large country have sleepwalked at least once in their lives. Suppose a random sample of 250 people showed that 60 reported sleepwalking. We will carry out the first two steps of a hypothesis test to determine if the proportion differs from 0.33, using a significance level of 0.05. **Step 1: Determine the Null and Alternative Hypotheses** - Null Hypothesis (H₀): \( p = 0.33 \) - Alternative Hypothesis (Hₐ): \( p \neq 0.33 \) (Enter integers or decimals. Do not round.) **Step 2: Check Conditions for the One-Proportion Z-Test** Select all the conditions that are not satisfied: - [ ] A. The Random Sample condition is not satisfied or cannot be reasonably assumed. - [ ] B. The Large Sample Size condition is not satisfied or cannot be reasonably assumed. - [ ] C. The Independence condition is not satisfied or cannot be reasonably assumed. - [x] D. The Large Population condition is not satisfied or cannot be reasonably assumed. - [ ] E. All conditions are satisfied or can be reasonably assumed. **Step 3: Identify Entries for Technology Input Figure** Fill in the values: - \( p_0 \): \( 0.33 \) - \( x \): \( 60 \) - \( n \): \( 250 \) - \( \text{prop} \): Not to be rounded. These values are essential inputs for statistical software or calculators used to perform the hypothesis test. The entries correspond to: - \( p_0 \): Hypothesized proportion - \( x \): Number of successes (people who reported sleepwalking) - \( n \): Total number of observations in the sample - prop: Sample proportion of successes (calculated as \( \frac{x}{n} \)) This educational content serves to guide through the initial steps of hypothesis testing focused on understanding population proportions and assessing statistical significance.
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