(a) What is the sample statistic? 0.2238 O 0.15 0.0857 O 0.007 (b) Which symbol is used for the statistic in this problem? π Ομ ор O 831 (c) Which hypotheses are being tested? O Ho: μ = 0.15 Ha: * 0.15 O Ho: π = 0.0857 Ha: 0.0857 O Ho: π = 0.15 Ha: π * 0.15 Hoπ = 0.007

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**Question (a):** What is the sample statistic?

- 0.2238 (selected)
- 0.15
- 0.0857
- 0.007

**Question (b):** Which symbol is used for the statistic in this problem?

- π
- μ
- p̂
- x̄

**Question (c):** Which hypotheses are being tested?

- H₀: μ = 0.15  
  Hₐ: μ ≠ 0.15

- H₀: π = 0.0857  
  Hₐ: π ≠ 0.0857

- H₀: π = 0.15  
  Hₐ: π ≠ 0.15

- H₀: π = 0.007
Transcribed Image Text:**Question (a):** What is the sample statistic? - 0.2238 (selected) - 0.15 - 0.0857 - 0.007 **Question (b):** Which symbol is used for the statistic in this problem? - π - μ - p̂ - x̄ **Question (c):** Which hypotheses are being tested? - H₀: μ = 0.15 Hₐ: μ ≠ 0.15 - H₀: π = 0.0857 Hₐ: π ≠ 0.0857 - H₀: π = 0.15 Hₐ: π ≠ 0.15 - H₀: π = 0.007
**Simulation of Proportion of Successes in Binomial Distribution**

**Parameters:**

- **Probability of success (π):** 0.15
- **Sample size (n):** 210
- **Number of samples:** 1000

**Options:**

- Animate the simulation process.
- Focus on the Proportion of successes.

**Inputs:**

- **As extreme as**: ≤ 0.0857 (threshold for comparison)
- Calculated **Proportion of samples**: (6 + 1) / 1000 = 0.0070

**Statistical Methods Selected:**

- Two-sided test for proportion values.
- Use of Exact Binomial distribution.
- Normal Approximation method.

**Graph Description:**

The graph depicts the distribution of the proportion of successes across 1000 samples. The x-axis represents the "Proportion of successes," ranging from approximately 0.08 to 0.23. The y-axis shows the frequency of samples, with a peak frequency of around 90.

- A normal distribution curve (in blue) overlays the frequency bars.
- Two red vertical lines indicate the cutoff points used in the analysis:
  - Left line at 0.0857
  - Right line at 0.2238
- The area under the curve for proportions less than or equal to 0.0857 is highlighted with a red label showing 0.0070, representing the proportion of samples as calculated.

**Additional Features:**

- Options to show previous results or enable sliders for dynamic adjustments.
Transcribed Image Text:**Simulation of Proportion of Successes in Binomial Distribution** **Parameters:** - **Probability of success (π):** 0.15 - **Sample size (n):** 210 - **Number of samples:** 1000 **Options:** - Animate the simulation process. - Focus on the Proportion of successes. **Inputs:** - **As extreme as**: ≤ 0.0857 (threshold for comparison) - Calculated **Proportion of samples**: (6 + 1) / 1000 = 0.0070 **Statistical Methods Selected:** - Two-sided test for proportion values. - Use of Exact Binomial distribution. - Normal Approximation method. **Graph Description:** The graph depicts the distribution of the proportion of successes across 1000 samples. The x-axis represents the "Proportion of successes," ranging from approximately 0.08 to 0.23. The y-axis shows the frequency of samples, with a peak frequency of around 90. - A normal distribution curve (in blue) overlays the frequency bars. - Two red vertical lines indicate the cutoff points used in the analysis: - Left line at 0.0857 - Right line at 0.2238 - The area under the curve for proportions less than or equal to 0.0857 is highlighted with a red label showing 0.0070, representing the proportion of samples as calculated. **Additional Features:** - Options to show previous results or enable sliders for dynamic adjustments.
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