Question
It is believed that more than 60% of voters from a certain region in Canada favor the free trade agreement. A recent poll indicated that out of 400 randomly selected individuals, 250 favored the free trade agreement. The null and alternative hypothesis would be:
Answers
GPT-4o mini
To formulate the null and alternative hypotheses for the given situation, we begin by defining the population proportion of voters who favor the free trade agreement:
- Let \( p \) represent the true proportion of voters in the region who favor the free trade agreement.
### Null and Alternative Hypotheses:
1. **Null Hypothesis (H0)**: The null hypothesis states that the true proportion of voters who favor the agreement is equal to or less than 60%. This can be written as:
\[
H_0: p \leq 0.60
\]
2. **Alternative Hypothesis (H1)**: The alternative hypothesis posits that the true proportion of voters who favor the agreement is greater than 60%. This can be expressed as:
\[
H_1: p > 0.60
\]
### Conclusion:
Thus, the null and alternative hypotheses are:
- \( H_0: p \leq 0.60 \)
- \( H_1: p > 0.60 \)
This set of hypotheses is appropriate as we are testing whether the proportion of supporters is indeed more than 60% based on the data from the poll.
- Let \( p \) represent the true proportion of voters in the region who favor the free trade agreement.
### Null and Alternative Hypotheses:
1. **Null Hypothesis (H0)**: The null hypothesis states that the true proportion of voters who favor the agreement is equal to or less than 60%. This can be written as:
\[
H_0: p \leq 0.60
\]
2. **Alternative Hypothesis (H1)**: The alternative hypothesis posits that the true proportion of voters who favor the agreement is greater than 60%. This can be expressed as:
\[
H_1: p > 0.60
\]
### Conclusion:
Thus, the null and alternative hypotheses are:
- \( H_0: p \leq 0.60 \)
- \( H_1: p > 0.60 \)
This set of hypotheses is appropriate as we are testing whether the proportion of supporters is indeed more than 60% based on the data from the poll.