# 04 the auditor should request a larger sample 859 a 1

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Since the upper bound is higher than the tolerable exception rate of 0.04, the auditor should request a larger sample.8.59(a) (1–)0.024(10.024)0.024+1.645500sspppZn0.0353p(b) With 95% level of confidence, the auditor can conclude that the rate of noncompliance is less than 0.0353, which is less than the 0.05 tolerable exception rate for internal control, and, hence, the internal control compliance is adequate.8 60The only way to have 100% confidence is to obtain the parameter of interest, rather than asample statistic. From another perspective, the range of the normal and tdistribution isinfinite, so a Zor tvalue that contains 100% of the area cannot be obtained.8.61The tdistribution is used for obtaining a confidence interval for the mean when unknown.8.62If the confidence level is increased, a greater area under the normal or tdistribution needs tobe included. This leads to an increased value of Zor t, and thus a wider interval.8.63The confidence interval will be narrower and the sample size will be smaller.8.64In some applications such as auditing, interest is primarily on the total amount of a variablerather than the average amount.8.65Difference estimation involves determining the difference between two amounts, rather thana single amount.
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161 Chapter 8: Confidence Interval Estimation8.66(a) (1–)0.43(0.57)0.431.965000ssspppZn0.4160.444pThe sampling error is 0.014.(b) (1–)0.159(10.159)0.1591.965000ssspppZn0.1490.169pThe sampling error is 0.010(c) The sampling error is the largest when 0.5sp. Hence, the sampling error of (a) with 0.43spis larger than that of (b) when 0.159sp8.67(a) The population from which this sample was drawn was the collection of all subscribers to the Redbook magazine who visited the magazine's web site.(b) The sample is not a random sample from this population. The sample consisted of only those subscribers to the magazine who visited the magazine's web site and chose to fill up the survey. (c) This is not a statistically valid study. There was selection bias since only those who visited the magazine's web site and chose to answer the survey were represented. There was possibly nonresponse bias as well. Visitors to the web site who chose to fill up the survey might not answer all questions and there was no way for the magazine to get back to them to follow-up on the nonresponses if this was an anonymous survey.(d) To avoid the above potential pitfalls, the magazine could drawn a random sample from the list of all subscribers to the magazine and offer them the option of filling upthe survey over the Internet or on the survey form that is mailed to the subscribers. The magazine should also keep track of the subscribers who are invited to fill in the survey and follow up on the nonresponses after a specified period of time with mail or telephone to encourage them to participate in the survey. The sample size needed is 2222(1–)1.96(0.6195) (0.6195)2264(0.02)Zppne 8.68(a) (1–)0.657(10.657)0.6571.96364ssspppZn0.6080.705p(b) 2222(1–)1.96(0.657) (0.657)2165(0.02)Zppne (c) (1–)0.870(10.870)0.8701.96239ssspppZn0.8280.913p(d) (1–)0.46(10.460)0.461.96239ssspppZn0.3970.523p