Describe the sampling distribution of p. Assume the size of the population is 25,000. n= 300, p = 0.4 Choose the phrase that best describes the shape of the sampling distribution of p below. A. Approximately normal because n s0.05N and np(1- p) < 10. 'B. Approximately normal because ns 0.05N and np(1- p) 2 10. O C. Not normal because ns0.05N and np(1 - p) 2 10. O D. Not normal because ns0.05N and np(1 - p) < 10.

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**Sampling Distribution of Proportion (\(\hat{p}\))**

**Problem Statement:**
Describe the sampling distribution of \(\hat{p}\). The population size is 25,000 with sample size \(n = 300\) and proportion \(p = 0.4\).

**Options:**

- **A.** Approximately normal because \(n \leq 0.05N\) and \(np(1-p) < 10\).
- **B.** Approximately normal because \(n \leq 0.05N\) and \(np(1-p) \geq 10\).
- **C.** Not normal because \(n \leq 0.05N\) and \(np(1-p) \geq 10\).
- **D.** Not normal because \(n \leq 0.05N\) and \(np(1-p) < 10\).

**Correct Answer:**
- **B.** Approximately normal because \(n \leq 0.05N\) and \(np(1-p) \geq 10\).

**Calculation Requirement:**
Determine the mean of the sampling distribution of \(\hat{p}\).

Mean (\(\mu_{\hat{p}}\)) Formula: \(\mu_{\hat{p}} = \frac{\mu}{p}\)

**Instruction:**
Round to one decimal place as needed.
Transcribed Image Text:**Sampling Distribution of Proportion (\(\hat{p}\))** **Problem Statement:** Describe the sampling distribution of \(\hat{p}\). The population size is 25,000 with sample size \(n = 300\) and proportion \(p = 0.4\). **Options:** - **A.** Approximately normal because \(n \leq 0.05N\) and \(np(1-p) < 10\). - **B.** Approximately normal because \(n \leq 0.05N\) and \(np(1-p) \geq 10\). - **C.** Not normal because \(n \leq 0.05N\) and \(np(1-p) \geq 10\). - **D.** Not normal because \(n \leq 0.05N\) and \(np(1-p) < 10\). **Correct Answer:** - **B.** Approximately normal because \(n \leq 0.05N\) and \(np(1-p) \geq 10\). **Calculation Requirement:** Determine the mean of the sampling distribution of \(\hat{p}\). Mean (\(\mu_{\hat{p}}\)) Formula: \(\mu_{\hat{p}} = \frac{\mu}{p}\) **Instruction:** Round to one decimal place as needed.
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