Questions: 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 1004 adults from Country A, 1068 adults from Country B, 1123 adults from Country C, and 1010 adults from Country D. At α=0.09, 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. Identify the claim and state H0 and Ha. The claim is "the proportion of adults in Country A who favor building new nuclear power plants in their country is the proportion of adults from Country B who favor building new nuclear power plants in their country."

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 1004 adults from Country A, 1068 adults from Country B, 1123 adults from Country C, and 1010 adults from Country D. At α=0.09, 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.

Identify the claim and state H0 and Ha.
The claim is "the proportion of adults in Country A who favor building new nuclear power plants in their country is the proportion of adults from Country B who favor building new nuclear power plants in their country."

Transcript text: 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 1004 adults from Country A, 1068 adults from Country B, 1123 adults from Country C, and 1010 adults from Country D. At $\alpha=0.09$, 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. Identify the claim and state $\mathrm{H}_{0}$ and $\mathrm{H}_{a}$. The claim is "the proportion of adults in Country A who favor building new nuclear power plants in their country is $\square$ the proportion of adults from Country B who favor building new nuclear power plants in their country."

Solution

Solution Steps

Step 1: Identify the claim

The claim is that the proportion of adults in Country A who favor building new nuclear power plants is _the same as_ the proportion of adults from Country B who favor building new nuclear power plants.

Step 2: State the null hypothesis H₀

The null hypothesis is that there is no difference between the proportions. In other words, the proportion of adults in Country A who favor building new nuclear power plants is the same as the proportion of adults from Country B. Symbolically, we can write this as:

_H₀: p₁ = p₂_

where p₁ represents the proportion of adults in Country A who favor building new nuclear power plants and p₂ represents the proportion of adults in Country B who favor the same.

Step 3: State the alternative hypothesis Hₐ

The alternative hypothesis is the opposite of the null hypothesis. Since the claim is that the proportions are the same, the alternative hypothesis is that the proportions are _different_. Symbolically, this can be written as:

_Hₐ: p₁ ≠ p₂_

Final Answer:

The claim states that the proportion of adults in Country A who favor building new nuclear power plants is the same as the proportion of adults in Country B. H₀: p₁ = p₂ Hₐ: p₁ ≠ p₂

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