A research center claims that at least 25% of adults in a certain country think that their taxes will be audited. In a random sample of 600 adults in that country in a recent year, 22% say they are concerned that their taxes will be audited. At α = 0.01, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below.
(a) Identify the claim and state H₀ and Hₐ.
Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or a decimal. Do not round.)
A. The percentage of adults in the country who think that their taxes will be audited is not %.
B. Less than % of adults in the country think that their taxes will be audited.
C. % of adults in the country think that their taxes will be audited.
D. At least % of adults in the country think that their taxes will be audited.
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 ≥
(b) Find the critical value(s) and identify the rejection region(s).
Identify the critical value(s) for this test.
z₀ =
(Round to two decimal places as needed. Use a comma to separate answers as needed.)
Identify the rejection region(s). Select the correct choice below and fill in the answer box(es) to complete your choice.
(Round to two decimal places as needed.)
A. The rejection region is z < .
B. The rejection region is < z < .
C. The rejection region is z > .
D. The rejection regions are z < and z > .
(c) Find the standardized test statistic z.
z =
(Round to two decimal places as needed.)
(d) Decide whether to reject or fail to reject the null hypothesis and (e) interpret the decision in the context of the original claim.
the null hypothesis. There enough evidence to the center's claim.