It is believed that 60% of voters from a certain region in South Africa favour the free trade agreement. A recent poll indicated that out of 400 randomly selected individuals, 250 favoured the free trade agreement. Test at 5% significance level if indeed at least 60% of voters favoured the FTA. State the null and alternative hypothesis.

Question

GPT-4o mini · Answer

To test whether at least 60% of voters favour the free trade agreement, we need to establish the null and alternative hypotheses.

Null Hypothesis (H₀): The proportion of voters who favour the free trade agreement is at least 60%. Mathematically, this can be stated as: \[ H₀: p \geq 0.60 \]

Alternative Hypothesis (H₁): The proportion of voters who favour the free trade agreement is less than 60%. This can be expressed as: \[ H₁: p < 0.60 \]

Summary of Hypotheses:

H₀: p ≥ 0.60
H₁: p < 0.60

Next steps:

To conduct the significance test, you would use a one-sample proportion test given that you have a sample proportion and want to compare it to the hypothesized population proportion.

You would calculate the sample proportion (\( \hat{p} \)), perform the test statistic calculations, and compare it to the critical value or compute the p-value to make a decision regarding the null hypothesis.