A superintendent of a school district in Pittsburgh wants to compare their student preference of chocolate milk over regular milk to students in New York City. A random sample of 258 students in Pittsburgh (Group 1) found that 57 preferred chocolate milk. A random sample of 474 students in New York City (Group 2) found that 154 preferred chocolate milk. You wish to test the claim that the proportion of all students in Pittsburgh is less than the proportion of all students in New York City that prefer chocolate milk at a significance level of $\displaystyle \alpha={0.10}$. Round answers to at least 4 decimal places.

What are the correct hypotheses?

H₀: Select an answer σ₁ x̅₂ p p₂ μ₁ x̅₁ p₁ μ₂ ? ≤ > ≠ < ≥ = Select an answer p₁ μ₁ p p₂ μ₂ x̅₂ σ₂ x̅₁ 0

H₁: Select an answer σ₁ μ₂ p₁ x̅₂ x̅₁ p₂ p μ₁ ? > ≠ ≥ = ≤ < Select an answer p₂ μ₁ p₁ x̅₁ 0 σ₁ x̅₂ p μ₂

Based on the hypotheses, find the following:

Test Statistic =

p-value =

The p-value is Select an answer less than (or equal to) alpha greater than alpha to alpha.

The correct decision is to Select an answer accept the alternative hypothesis reject the claim fail to reject the null hypothesis reject the null hypothesis accept the null hypothesis .

The correct summary would be: Select an answer There is not enough evidence to reject There is enough evidence to support There is enough evidence to reject There is not enough evidence to support the claim that the proportion of all students in Pittsburgh is less than the proportion of all students in New York City that prefer chocolate milk.