A research center claims that at least 45% of adults in a certain country think

Question

A research center claims that at least 45% of adults in a certain country think the government is not aggressive aton their taxes. a 0.01.is there enough evidence to reject the center's claim? Complete parts (a) through (e) below (a) Identify the claim and state Ho and H. What is the claim? O A- least 45% of all adults think the government is not aggressive enough in pursuing people who cheat on taxes. B. Exactly 39% of al aduts think the government is their taxes. not aggressive enough in pursuing people who cheat on their O c. Exactly 39% of adults in the country think the govemmert is not aggressive enough in pursuing people who cheat on their taxes. ts in the country think the government is not aggressive enough in pursuing people who cheat on their taxes identity Ho and Ha (Type integers or decimals) Find the critical value(s) and identify the rejecton regors) The critical values) is/are zo Click to select your answers TOSHIBA s tem that country, say t

Explanation / Answer

Solution:-

a) The claim is Atleast 45% of the adult think that government is not agressive enough in pursuing people who cheat on their taxes.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P > 0.45

Alternative hypothesis: P < 0.45

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).

= sqrt[ P * ( 1 - P ) / n ]

= 0.0188

b) zcritical = - 2.33

Rejection region:-

We will reject the null hypothesis if z value is less than - 2.33

z = (p - P) /

c) z = - 3.19

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a one-tailed test, the P-value is the probability that the z-score is less than -1.75. We use the Normal Distribution Calculator to find P(z < -1.75) = 0.04. Thus, the P-value = 0.04.

Interpret results. Since the z value lies in rejection region, we cannot accept the null hypothesis.

d) Reject the null hypothesis, There is not enough evidence at 1% level of significance to accept the center's claim that atleast 45% of the adult thimk that the government is not aggressive enough in pursuing people who cheat on their taxes.

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