A research center claims that at least 30% of adults in a certain country think that their taxes will be audited. In a random sample of 1000 adults in that country in a recent year, 26% say they are concerned that their taxes will be audited. At a = 0.01, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. %3D B. The rejection region is z< - 2.33. C. The rejection region is (c) Find the standardized test statistic z. Z= (Round to two decimal places as needed.) Enter your answer in the answNer hox and then cliolk Chool 0

Introduction: Denote p as the true proportion of adults who believe that their taxes will be audited in a recent year. A it is of interest to know whether at least 30% or 0.30 proportion believe that their taxes will be audited, the null and alternative hypotheses are: H0: p ≥ 0.30; H1: p < 0.30. Calculation: Due to the large sample size of 1,000, an approximate normal distribution of the sample proportions may be assumed, so that the z-test can be used. The left-tailed z-test for testing the significance of a proportion may be used here, as the alternative is of the greater-than type. The sample size is, n = 1,000 adults. Considering finding an adult who believes that their taxes will be audited, the sample proportion of successes is, p̂ = 0.26 that is, 26%. The z-test statistic is: z = p^ – pp1-pn = 0.26 – 0.300.31-0.31000 = –0.040.00021 ≈ –2.76. Thus, the value of the test statistic is –2.76. The significance level is given as, α = 0.01. For significance level α, the critical value for the left-tailed z-test is –zα, such that, P (Z ≤ zα) = α. This implies that, P (Z ≤ z0.01) = 0.01. Using the standard normal distribution table or the Excel formula: =NORM.S.INV(0.01), it can be found that –z0.01 = –2.33. Thus, the critical value is z0 = –zα = –2.33. Decision rule for the left-tailed test using critical values: Reject H0 at significance level α, if z ≤ z0. Otherwise, fail to reject H0. The decision rule here is: Reject H0 at significance level α, if z ≤ –2.33. Otherwise, fail to reject H0. Thus, the rejection region is z < –2.33. Here, z (= –2.76) < z0 (= –2.33). Hence, we reject the null hypothesis, at α = 0.01. Thus, there is enough evidence to reject the centers claim at 0.01 level.