Use the figure to the right, which shows the percentages of adults from several countries who favor building new nuclear power plants in their country. The survey included random samples of 1047 adults from Country A, 1070 adults from Country B, 1128 adults from Country C, and 1026 adults from Country D. At a=0.06, can you reject the dlaim that the proportion 100 of adults in Country A who favor bulding new nuciear power plants in their country is the same as the proportion of adults from Country B who favor building new nuciear power plants in 80 60 40 20 their country? Assume the random samples are independent. Country A 49% Country B 51 Country C 44% OCountry D 36% ....

MATLAB: An Introduction with Applications
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Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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**Identify the claim and state \( H_0 \) and \( H_a \).**

The claim is "the proportion of adults in Country A who favor building new nuclear power plants in their country is the same as the proportion of adults from Country B who favor building new nuclear power plants in their country."

Let \( p_1 \) represent the population proportion for Country A and \( p_2 \) represent the population proportion for Country B. State \( H_0 \) and \( H_a \).

**Choose the correct answer below:**

- A. \( H_0: p_1 > p_2 \)  
     \( H_a: p_1 < p_2 \)

- B. \( H_0: p_1 = p_2 \)  
     \( H_a: p_1 \neq p_2 \)

- C. \( H_0: p_1 \neq p_2 \)  
     \( H_a: p_1 = p_2 \)

- D. \( H_0: p_1 < p_2 \)  
     \( H_a: p_1 > p_2 \)

- E. \( H_0: p_1 = p_2 \)  
     \( H_a: p_1 < p_2 \) ✓

- F. \( H_0: p_1 = p_2 \)  
     \( H_a: p_1 > p_2 \)

---

Find the standardized test statistic.

\[ z = 1.84 \] (Round to two decimal places as needed.)

---

Use technology to calculate the P-value.

\[ \text{P-value} = 0.066 \] (Round to three decimal places as needed.)

---

**Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below.**

- Fail to reject \( H_0 \) because the P-value is less than the significance level \( \alpha \).
- Fail to reject \( H_0 \) because the P-value is greater than the significance level \( \alpha \).
- Reject \( H_0 \) because the P-value is less than the significance level \( \alpha \).
- Reject \( H_0 \) because the P-value is greater than the significance level \( \alpha \).

**Can you reject the original claim? Choose the correct answer below.**

- A
Transcribed Image Text:**Identify the claim and state \( H_0 \) and \( H_a \).** The claim is "the proportion of adults in Country A who favor building new nuclear power plants in their country is the same as the proportion of adults from Country B who favor building new nuclear power plants in their country." Let \( p_1 \) represent the population proportion for Country A and \( p_2 \) represent the population proportion for Country B. State \( H_0 \) and \( H_a \). **Choose the correct answer below:** - A. \( H_0: p_1 > p_2 \) \( H_a: p_1 < p_2 \) - B. \( H_0: p_1 = p_2 \) \( H_a: p_1 \neq p_2 \) - C. \( H_0: p_1 \neq p_2 \) \( H_a: p_1 = p_2 \) - D. \( H_0: p_1 < p_2 \) \( H_a: p_1 > p_2 \) - E. \( H_0: p_1 = p_2 \) \( H_a: p_1 < p_2 \) ✓ - F. \( H_0: p_1 = p_2 \) \( H_a: p_1 > p_2 \) --- Find the standardized test statistic. \[ z = 1.84 \] (Round to two decimal places as needed.) --- Use technology to calculate the P-value. \[ \text{P-value} = 0.066 \] (Round to three decimal places as needed.) --- **Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below.** - Fail to reject \( H_0 \) because the P-value is less than the significance level \( \alpha \). - Fail to reject \( H_0 \) because the P-value is greater than the significance level \( \alpha \). - Reject \( H_0 \) because the P-value is less than the significance level \( \alpha \). - Reject \( H_0 \) because the P-value is greater than the significance level \( \alpha \). **Can you reject the original claim? Choose the correct answer below.** - A
**Transcription for Educational Website**

---

**Survey Analysis on Nuclear Power Plant Support**

Use the figure to the right, which shows the percentages of adults from several countries who favor building new nuclear power plants in their country. The survey included random samples of 1047 adults from Country A, 1070 adults from Country B, 1128 adults from Country C, and 1026 adults from Country D. At α = 0.08, can you reject the claim that the proportion of adults in Country A who favor building new nuclear power plants in their country is the same as the proportion of adults from Country B who favor building new nuclear power plants in their country? Assume the random samples are independent.

**Bar Graph Explanation**

- The bar graph displays the percentages of adults favoring new nuclear power plants for each country:
  - **Country A**: 49% favor
  - **Country B**: 51% favor
  - **Country C**: 44% favor
  - **Country D**: 36% favor

**Hypothesis Testing**

Identify the claim and state \( H_0 \) and \( H_a \).

The claim is "the proportion of adults in Country A who favor building new nuclear power plants in their country is [select an option: equal to, not equal to, greater than, less than] the proportion of adults from Country B who favor building new nuclear power plants in their country."

--- 

In this context, the essence of the study is to determine if there's statistical evidence to support the difference in proportions between Country A and Country B at a significance level of 0.08.
Transcribed Image Text:**Transcription for Educational Website** --- **Survey Analysis on Nuclear Power Plant Support** Use the figure to the right, which shows the percentages of adults from several countries who favor building new nuclear power plants in their country. The survey included random samples of 1047 adults from Country A, 1070 adults from Country B, 1128 adults from Country C, and 1026 adults from Country D. At α = 0.08, can you reject the claim that the proportion of adults in Country A who favor building new nuclear power plants in their country is the same as the proportion of adults from Country B who favor building new nuclear power plants in their country? Assume the random samples are independent. **Bar Graph Explanation** - The bar graph displays the percentages of adults favoring new nuclear power plants for each country: - **Country A**: 49% favor - **Country B**: 51% favor - **Country C**: 44% favor - **Country D**: 36% favor **Hypothesis Testing** Identify the claim and state \( H_0 \) and \( H_a \). The claim is "the proportion of adults in Country A who favor building new nuclear power plants in their country is [select an option: equal to, not equal to, greater than, less than] the proportion of adults from Country B who favor building new nuclear power plants in their country." --- In this context, the essence of the study is to determine if there's statistical evidence to support the difference in proportions between Country A and Country B at a significance level of 0.08.
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