Hypotheses Testing

Question

You want to see if the proportion of the population that wants the government to enact stronger measures to counteract climate change is different between those under 40 and those 40 and over. You sample 150 people under the age of 40, and 100 want to see stronger measures. Of those 40 and older, you ask 175, and find 95 want stronger measures taken. Perform a test at the level α = 0.05.

Answer 1

H₀​: p₁ = p₂​ (The proportions are equal between the two groups)

H_a​: p₁ ≠ p₂​ (The proportions are different between the two groups)

Where:

1. p₁​ = proportion of people under 40 who want stronger measures
2. p₂​ = proportion of people 40 and over who want stronger measures

Then, use 2-PropZTest on the TI-84 with the following inputs:

1. x₁ = 100, n₁ = 150
2. x₂ = 95, n₂ = 175
3. p₁ ≠ p₂

The p-value is 0.023. α = 0.05. Since p < α, we reject the null hypothesis. There is sufficient evidence to conclude that the proportion of people who want stronger measures to counteract climate change is different between those under 40 and those 40 and over.

Hope this was helpful.