Because of the complex nature of the U.S.income tax system,many people have questions for the Internal Revenue Service (IRS).Yet,an article published by the Detroit Free Press entitled "Assistance: IRS Help Centers Give the Wrong Information" discusses the propensity of IRS staff employees to give incorrect tax information to tax-payers who call with questions.Then IRS Inspector General Pamela Gardiner told a Senate subcommittee that "the IRS employees at 400 taxpayer assistance centers nationwide encountered 8.5 million taxpayers face-to-face last year.The problem: When inspector general auditors posing as taxpayers asked them to answer tax questions,the answers were right 69% of the time." Suppose an independent commission was formed to test whether the 0.69 accuracy rate is correct or whether it is actually higher or lower.The commission has randomly selected n = 180 tax returns that were completed by IRS assistance employees and found that 105 of the returns were accurately completed. Using an α= 0.05 level,based on the sample data,what conclusion should be reached about the IRS rate of correct tax returns? A)The z-critical values from the standard normal table for a two-tailed test with alpha = 0.05 are And z = -1.96.Since z = -0.96 -1.96,we do not reject the null hypothesis.Thus,based on these sample data,we believe that the accuracy rate is actually higher than the 0.69 rate quoted in the Detroit Free Press article B)The z-critical values from the standard normal table for a two-tailed test with alpha = 0.05 are And z = -1.96.Since z = -0.96 -1.96,we do not reject the null hypothesis.Thus,based on these sample data,we believe that the accuracy rate is actually higher than the 0.58 rate quoted in the Detroit Free Press article C)The z-critical values from the standard normal table for a two-tailed test with alpha = 0.05 are And z = -1.96.Since z= -3.19

Question

Because of the complex nature of the U.S.income tax system,many people have questions for the Internal Revenue Service (IRS).Yet,an article published by the Detroit Free Press entitled "Assistance: IRS Help Centers Give the Wrong Information" discusses the propensity of IRS staff employees to give incorrect tax information to tax-payers who call with questions.Then IRS Inspector General Pamela Gardiner told a Senate subcommittee that "the IRS employees at 400 taxpayer assistance centers nationwide encountered 8.5 million taxpayers face-to-face last year.The problem: When inspector general auditors posing as taxpayers asked them to answer tax questions,the answers were right 69% of the time." Suppose an independent commission was formed to test whether the 0.69 accuracy rate is correct or whether it is actually higher or lower.The commission has randomly selected n = 180 tax returns that were completed by IRS assistance employees and found that 105 of the returns were accurately completed.
Using an α= 0.05 level,based on the sample data,what conclusion should be reached about the IRS rate of correct tax returns?
A)The z-critical values from the standard normal table for a two-tailed test with alpha = 0.05 are And z = -1.96.Since z = -0.96 > -1.96,we do not reject the null hypothesis.Thus,based on these sample data,we believe that the accuracy rate is actually higher than the 0.69 rate quoted in the Detroit Free Press article 
B)The z-critical values from the standard normal table for a two-tailed test with alpha = 0.05 are And z = -1.96.Since z = -0.96 > -1.96,we do not reject the null hypothesis.Thus,based on these sample data,we believe that the accuracy rate is actually higher than the 0.58 rate quoted in the Detroit Free Press article 
C)The z-critical values from the standard normal table for a two-tailed test with alpha = 0.05 are And z = -1.96.Since z= -3.19 < -1.96,we reject the null hypothesis.Thus,based on these sample data,we believe that the accuracy rate is actually lower than the 0.69 rate quoted in the Detroit Free Press article. 
D)The z-critical values from the standard normal table for a two-tailed test with alpha = 0.05 are

Quizplus · Accepted Answer

We are given that n = 180 and out of these 105 were accurately completed. The sample proportion (p̂) of accurately completed tax returns can be calculated as p̂ = 105/180 = 0.583. We need to test whether this sample proportion provides sufficient evidence to reject the null hypothesis that the true proportion of accurately completed tax returns is equal to 0.69, as claimed by the Detroit Free Press article.

The null hypothesis is H0: p = 0.69 and the alternative hypothesis is Ha: p < 0.69 (since we are testing whether the accuracy rate is actually lower than 0.69). Since the sample size is large and we are testing for proportion, we can use the normal distribution to compute the test statistic.

The test statistic is given by z = (p̂ - p0) / sqrt(p0 * (1 - p0) / n), where p0 = 0.69 is the hypothesized proportion under the null hypothesis. Substituting the values, we get z = (0.583 - 0.69) / sqrt(0.69 * 0.31 / 180) = -3.19 (rounded to two decimal places).

The z-critical value for a two-tailed test with α = 0.05 is ±1.96. Since our alternative hypothesis is one-tailed (p < 0.69), we reject the null hypothesis if the calculated z-value is less than -1.96. Since our calculated z-value of -3.19 is less than -1.96, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the accuracy rate is actually lower than the 0.69 rate quoted in the Detroit Free Press article.

Because of the Complex Nature of the U