Question

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=0.100.10​,

is there enough evidence to reject the​ center's claim? Complete parts​ (a) through​(e) below.

Answer 1

Claim: A research center claims that at least 25% of adults in a certain country think that their taxes will be audited.

That is

The claim comes under the null hypothesis. and the alternative hypothesis contains the exact opposite sign of greater than equal to, that is less than.

(a) Null and alternative hypothesis:

(b) Critical value:

The alternative hypothesis contains less than sign so the test is left tailed test.

alpha = 0.10

For the left tailed test, just search alpha 0.10 in the middle body of the z table and take the corresponding row and column number.

The z score for area 0.10 is -1.28, for left tailed test the critical value is negative.

z critical value = -1.28

(c) z test statistics:

The formula to find the z test statistics is,

where

p = population proportion = 0.25 and n = sample size = 600

z test statistics = -1.70

(d) Decision:

Decision rule: If |z critical value| > |z test statistics| then fail to reject the null hypothesis otherwise reject the null hypothesis.

|z critical value| = |-1.28| = 1.28 and |z test statistics| = |-1.70| = 1.70

So, |z criitcal| is not greater than |Z test statistics|, so reject the null hypothesis.

(e) Conclusion:

Reject the null hypothesis, that is there is not sufficient evidence to support the claim that at least 25% of adults in a certain country think that their taxes will be audited.

Yes, there is enough evidence to reject the center's claim.