Question

a research center claims that at least 30% of adults in a certain country think that their taxes will be audited. in a random sample of 1100 adults in that country in a recent year, 25% say they are concerned that their taxes will be audited. at α=0.05, is there enough evidence to reject the centers claim? complete parts (a) through (d) below. let p be the population proportion of successes, where a success is an adult in the country who thinks that their taxes will be audited. state h₀ and hₐ. select the correct choice below and fill in the answer boxes to complete your choice. (round to two decimal places as needed.) a. h₀: p< hₐ: p≥ b. h₀: p= hₐ: p≠ c. h₀: p≠ hₐ: p= d. h₀: p> hₐ: p≤ e. h₀: p≤ hₐ: p> f. h₀: p≥ hₐ: p<

Explanation:

Step1: Identify the claim

The research center claims that at least 30% (0.30) of adults think their taxes will be audited. So the null hypothesis \( H_0 \) should contain this claim (or its complement for the alternative). The alternative hypothesis \( H_a \) is what we are testing against, which would be that the proportion is less than 0.30 if we are rejecting the claim of at least 0.30.

Step2: Determine \( H_0 \) and \( H_a \)

The claim is \( p \geq 0.30 \), so the null hypothesis \( H_0 \) is \( p \geq 0.30 \) (since the null hypothesis typically includes the equality or the claim we are testing). The alternative hypothesis \( H_a \) is the opposite, which is \( p < 0.30 \). Looking at the options, option F has \( H_0: p \geq 0.30 \) and \( H_a: p < 0.30 \).

Answer:

F. \( H_0: p \geq 0.30 \), \( H_a: p < 0.30 \)