Question

a research center claims that at least 29% of adults in a certain country think that their taxes will be audited. in a random sample of 800 adults in that country in a recent year, 26% say they are concerned that their taxes will be audited. at \\( \alpha = 0.10 \\), is there enough evidence to reject the centers claim? complete parts (a) through (d) below. (a) identify the claim and state \\( h _ { 0 } \\) and \\( h _ { a } \\). 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.) \\( \bigcirc \\) a. at least \\( \\% \\) of adults in the country think that their taxes will be audited. \\( \bigcirc \\) b. the percentage of adults in the country who think that their taxes will be audited is not \\( \\% \\). \\( \bigcirc \\) c. \\( \\% \\) of adults in the country think that their taxes will be audited. \\( \bigcirc \\) d. less than \\( \\% \\) of adults in the country think that their taxes will be audited.

Explanation:

The research center's claim is "at least 29% of adults in a certain country think that their taxes will be audited". In hypothesis testing, the null hypothesis \(H_0\) is a statement of equality or a statement that is assumed to be true, and the alternative hypothesis \(H_a\) is a statement that we are trying to find evidence for.

For a proportion \(p\), if the claim is \(p\geq p_0\) (in this case \(p_0 = 0.29\)), the null hypothesis \(H_0:p\geq0.29\) and the alternative hypothesis \(H_a:p < 0.29\) (since we are testing against the claim to see if there is enough evidence to reject it).

Answer:

A. At least \(29\)% of adults in the country think that their taxes will be audited.
\(H_0:p\geq0.29\), \(H_a:p < 0.29\)