A sample in which the characteristics of the sample are the same as those of the population is: A) an attributes sample. B) a variables sample. C) a representative sample. D) a random sample. 2) One of the causes of non-sampling error is: A) the use of inappropriate or ineffective audit procedures. B) the use of attributes sampling instead of variables sampling. C) failure to draw a random sample. D) failure to draw a representative sample. 3) How can non-sampling risk be eliminated? A) proper supervision and instruction of the client's employees B) controls which ensure that the sample drawn is random and representative C) the use of attributes sampling rather than variables sampling D) proper supervision and instruction of the audit team 4) Sampling risk (sampling error) is an inherent part of sampling which results from: A) testing less than the entire population. B) weaknesses in client's internal control system. C) inappropriate audit procedures. D) failure to recognise exceptions. 5) Non-sampling errors occur when audit tests do NOT uncover existing exceptions in the: A) planning stage. B) population. C) financial statements. D) sample. 6) One of the ways to reduce sampling risk is to: A) provide proper supervision and instruction of the audit team. B) carefully design the audit procedures to be used. C) use variables sampling rather than attributes sampling. D) use an appropriate method of selecting sample items from the population. 7) Which one of the following BEST illustrates the concept of sampling risk? A) The documents related to the chosen sample may not be available for inspection. B) An auditor may select audit procedures that are not appropriate to achieve the specific objective. C) A randomly chosen sample may not be representative of the population as a whole on the characteristics of interest. D) An auditor may fail to recognise errors in the documents examined for the chosen sample. 8) The risk which the auditor is willing to take in accepting a control as being effective when it is not is the: A) allowable risk of overreliance (ARO). B) tolerable deviation rate (TDR). C) estimated population deviation rate. D) sample deviation rate (SDR). 9) The deviation rate the auditor will permit in the population and still be willing to use the assessed level of control risk established during planning is called the: A) tolerable deviation rate (TDR). B) sample deviation rate (SDR). C) acceptable risk of overreliance (ARO). D) estimated population deviation rate. 10) What is the most important aspect of audit sampling? A) evaluating the results B) sample selection C) performing the audit procedures D) all of the above
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a. Sample selection bias: a. Is only important for finite sample results b. Occurs when a selection process influences the availability of data and that process is related to the dependent variable c. Results in the OLS estimator being biased, although it is still consistent d. Is more important for non-linear least squares estimation than for OLS 2. Which of the following problems will not cause the endogeneity problem in a linear regression model? a. Omitting relevant variables b. Including irrelevant variables c. Errors in variables d. Simultaneous equations 3. The following is not a threat to external validity a. The treatment being studied is not representative of the treatment that would be implemented more broadly b. Experimental participants are volunteers c. The experimental sample is not representative of the population of interest d. Partial compliance with the treatment protocol 4. The conditions for valid instruments do not include the following: a. Perfect multicollinearity between the predicted endogenous variables and the exogenous variables must be ruled out b. Each one of the instrumental variables must be normally distributed c. Each instrument must be uncorrelated with the error term d. At least one of the instruments must enter the population regression of X and the Z's and the W's. 5. A study based on the OLS regressions is internally valid if: a. The errors are homoscedastic, and there are no more than two binary variables present among the regressors b. You use a two-sided alternative hypothesis and standard errors are calculated using the heteroskedasticity robust formula c. Weighted least squares produces similar results and the t-statistics is normally distributed in large samples d. The OLS estimator is unbiased and consistent and the standard errors are computed in a way that makes the confidence intervals have the desired confidence level 6. The following will not cause a correlation between X and u in the simple regression model: a. Irrelevance of the regressor b. Simultaneous causality c. Omitted variables d. Errors in variables 7. The distinction between endogenous and exogenous variables is a. Dependent on the distribution of the variables, i.e., when they are normally distributed, they are exogenous, otherwise, they are endogenous. b. Whether or not the variables are correlated with the error term c. That exogenous variables are determined inside the model and endogenous variables are determined outside of the model d. Dependent on the sample size, i.e., for n sufficiently large, endogenous variables become exogenous 8. The reliability of a study using a multiple regression analysis depends on all of the following with the exception of: a. Omitted variable bias b. External validity c. Presence of homoskedasticity in the error term d. Errors in variables
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1. Parametric statistics are appropriate when: Select one: a. the sample size is small. b. the data are nominal data. c. the sampling distribution is normally distributed d. All of the above. 2. The is a symmetrical, bell‑shaped distribution that is contingent on sample size. It has a mean of zero and a standard deviation equal to one. Select one: a. chi square distribution b. t distribution c. ANOVA d. F distribution 3. In the legal profession, a Type I error would be equivalent to: Select one: a. none of the above. b. flipping a coin to determine if a man goes to prison or not c. sending an innocent man to prison d. setting a guilty party free 4. All of the following are steps involved in calculating the chi‑square statistic, EXCEPT: Select one: a. Calculate the chi square value. b. Formulate the null hypothesis and determine the expected frequency of each answer. c. Calculate the sample mean. d. Determine the appropriate significance level. 5. The idea that “there is a significant difference in brand preference between males with incomes under $50,000 and males with incomes over $50,000” is an example of: Select one: a. Type II error. b. the alternative hypothesis. c. Type I error. d. the null hypothesis. 6. What type of error is made when the null hypothesis is false, but is not rejected? Select one: a. Type III b. Type I c. Type II d. sampling error 7. Statistically describing the relationship between two variables at one time, such as sales volume and gross national product, requires . Select one: a. univariate data analysis b. bivariate data analysis c. nonparametric data analysis d. multivariate data analysis 8. The idea that “there is no difference in buying behavior between males and females in the age group 25-49” is an example of: Select one: a. the alternative hypothesis. b. the null hypothesis. c. Type I error. d. Type II error. 9. A private art museum sponsoring a program of summer art classes for children expects an equal number of boys and girls. A random sample of its list of students shows there are more girls than boys. The appropriate univariate test for statistical significance is the: Select one: a. t test b. chi square test c. F-test d. Z test. 10. The region of ______________ shows those values that are very unlikely to occur if the null hypothesis is true, but relatively probable if the alternative hypothesis is true. Select one: a. rejection b. nonparametric c. alternatives d. acceptance
Expand Your Knowledge: Logarithmic Transformations, Exponential Growth Model There are several extensions of linear regression that apply to exponential growth and power law models. Problems 22-25 will outline some of these extensions. First of all, recall that a variable grows linearly over time if it adds a fixed increment during each equal time period. Exponential growth occurs when a variable is multiplied by a fixed number during each time period. This means that exponential growth increases by a fixed multiple or percentage of the previous amount. College algebra can be used to show that if a variable grows exponentially, then its logarithm grows linearly. The exponential growth model is $y=\alpha \beta^{x}$, where $\alpha$ and $\beta$ are fixed constants to be estimated from data. How do we know when we are dealing with exponential growth, and how can we estimate $\alpha$ and $\beta$ ? Please read on. Populations of living things such as bacteria, locusts, fish, panda bears, and so on, tend to grow (or decline) exponentially. However, these populations can be restricted by outside limitations such as food, space, pollution, disease, hunting, and so on. Suppose we have data pairs $(x, y)$ for which there is reason to believe the scatter plot is not linear, but rather exponential, as described above. This means the increase in $y$ values begins rather slowly but then seems to explode. Note: For exponential growth models, we assume all $y>0$. $$ \begin{array}{|l|lrrrr} \hline x & 1 & 2 & 3 & 4 & 5 \\ \hline y & 3 & 12 & 22 & 51 & 145 \\ \hline \end{array} $$ Consider the following data, where $x=$ time in hours and $y=$ number of bacteria in a laboratory culture at the end of $x$ hours. (a) Look at the Excel graph of the scatter diagram of the $(x, y)$ data pairs. Do you think a straight line will be a good fit to these data? Do the $y$ values seem almost to explode as time goes on? (b) Now consider a transformation $y^{\prime}=\log y .$ We are using common logarithms of base 10 (however, natural logarithms of base $e$ would work just as well). Consider the following data, where $x=$ time in hours and $y=$ number of bacteria in a laboratory culture at the end of $x$ hours. (a) Look at the Excel graph of the scatter diagram of the $(x, y)$ data pairs. Do you think a straight line will be a good fit to these data? Do the $y$ values seem almost to explode as time goes on? (b) Now consider a transformation $y^{\prime}=\log y .$ We are using common logarithms of base 10 (however, natural logarithms of base $e$ would work just as well). $$ \begin{array}{l|lllll} \hline x & 1 & 2 & 3 & 4 & 5 \\ \hline y^{\prime}=\log y & 0.477 & 1.079 & 1.342 & 1.748 & 2.161 \\ \hline \end{array} $$ Look at the Excel graph of the scatter diagram of the $\left(x, y^{\prime}\right)$ data pairs and compare this diagram with the diagram in part (a). Which graph appears to better fit a straight line? (c) Use a calculator with regression keys to verify the linear regression equation for the $(x, y)$ data pairs, $\hat{y}=-50.3+32.3 x$, with sample correlation coefficient $r=0.882$. (d) Use a calculator with regression keys to verify the linear regression equation for the $\left(x, y^{\prime}\right)$ data pairs, $y^{\prime}=0.150+0.404 x$, with sample correlation coefficient $r=0.994$. The sample correlation coefficient $r=0.882$ for the $(x, y)$ pairs is not bad. But the sample correlation coefficient $r=0.994$ for the $\left(x, y^{\prime}\right)$ pairs is a lot better! (e) The exponential growth model is $y=\alpha \beta^{x}$. Let us use the results of part (d) to estimate $\alpha$ and $\beta$ for this strain of laboratory bacteria. The equation $y^{\prime}=a+b x$ is the same as $\log y=a+b x .$ If we raise both sides of this equation to the power 10 and use some college algebra, we get $y=10^{a}\left(10^{b}\right)^{x}$. Thus, $\alpha \approx 10^{a}$ and $\beta \approx 10^{b}$. Use these results to approximate $\alpha$ and $\beta$ and write the exponential growth equation for our strain of bacteria. Note: The TI-84Plus/TI-83Plus/TI-nspire calculators fully support the exponential growth model. Place the original $x$ data in list $\mathrm{L} 1$ and the corresponding $y$ data in list L2. Then press STAT, followed by $\mathbf{C A L C}$, and scroll down to option $\mathbf{0}$ : ExpReg. The output gives values for $\alpha, \beta$, and the sample correlation coefficient $r$.
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