Question

A research center claims that at least 31% of adults in a certain country think that their taxes will be audited. In a random sample of 700 adults in that country in a recent year, 27% say they are concerned that their taxes will be audited. At alphaαequals=0.10, is there enough evidence to reject the center's claim? Complete parts (a) through(e) below.

(c) Find the standardized test statistic 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.

(Fail to reject/ Reject) the null hypothesis. There (is/ is not) enough evidence to support the researcher's claim.

Please explain your answers, as I do not understand how to do this! Thank you :)

Answer #1

The following information is provided: The sample size is N=700, the number of favorable cases is X=189, and the sample proportion is , and the significance level is α=0.10

The z-statistic is computed as follows:

**Reject** the null hypothesis. There
**is** enough evidence to support the researcher's
claim. Hence there is enough evidence to claim that the percentage
of people who think that their taxed will be audited is different
than 31%. Hence center's claim is rejected.

Since it is observed that
**∣z∣=2.288>zc=1.64**, it is then concluded that
*the null hypothesis is rejected.*

It is concluded that the null hypothesis Ho is
*rejected.* Therefore, there is enough evidence to claim
that the population proportion p is different than p0, at the
α=0.10 significance level.

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