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.