Question

question 1
recently, the price of gasoline was near the four - dollar mark in many parts of the united states. a survey indicated that 32% of americans curtailed their travel plans because of the price of gasoline. in fact, some experts claim that the number was even higher. a survey was done to test this claim. the survey revealed that 175 of 500 respondents were planning on traveling less because of high gasoline prices.
what are the null and alternate hypotheses for this test?

• $h_0: p \geq 0.32$ $h_a: p < 0.32$
• $h_0: p = 0.00$ $h_a: p \

eq 0.00$

• $h_0: p = 0.32$ $h_a: p > 0.32$
• $h_0: p \leq 0.24$ $h_a: p > 0.24$

Explanation:

Step1: Identify the claim

The original survey said 32% (p = 0.32) of Americans curtailed travel. Experts claim the number is higher. So we test if p > 0.32.

Step2: Define hypotheses

Null hypothesis (\(H_0\)) is the status quo or equality, here \(H_0: p = 0.32\) (or \(p \leq 0.32\) in some cases, but since the claim is higher, alternate (\(H_a\)) is \(p > 0.32\)). Checking options, the third option has \(H_0: p = 0.32\) and \(H_a: p > 0.32\), which matches.

Answer:

\(H_0: p = 0.32\) \(H_a: p > 0.32\) (the third option: \(H_0: p = 0.32\) \(H_a: p > 0.32\))