Question

1. a research center claims that at least 28% 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.

(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.)
a. the percentage of adults in the country who think that their taxes will be audited is not (square%).
b. (square%) of adults in the country think that their taxes will be audited.
c. at least (square%) of adults in the country think that their taxes will be audited.
d. less than (square%) 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 ( h_0 ) and ( h_a ). select the correct choice below and fill in the answer boxes to complete your choice.
(round to two decimal places as needed.)
a. ( h_0: p
eq square )
( h_a: p = square )
b. ( h_0: p < square )
( h_a: p geq square )
c. ( h_0: p > square )
( h_a: p leq square )
d. ( h_0: p = square )
( h_a: p > square )
e. ( h_0: p
eq square )
( h_a: p = square )
f. ( h_0: p geq square )
( h_a: p < square )

Explanation:

The claim is "At least 28% of adults in the country think that their taxes will be audited". In hypothesis testing, the null hypothesis \(H_0\) is a statement of equality or no - difference, and the alternative hypothesis \(H_a\) is the claim we are trying to find evidence for. For a proportion \(p\), if the claim is \(p\geq0.28\), the null hypothesis (which is the opposite of the alternative in a way that allows for a single - sided test) is \(H_0:p = 0.28\) and the alternative hypothesis is \(H_a:p<0.28\) (since we are testing against the "at least" claim, and in hypothesis testing for proportions, we set up the null as the boundary value of the claim when the claim is of the form \(p\geq k\) or \(p\leq k\)).

Answer:

The claim is "At least 28% of adults in the country think that their taxes will be audited".
For the hypotheses, if we let \(p\) be the proportion of adults who think their taxes will be audited:

• \(H_0:p = 0.28\)
• \(H_a:p<0.28\)