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# Chapter 21—Univariate Statistical Analysis. All Answers

Chapter 21—Univariate Statistical Analysis 1. Univariate statistical analysis tests hypotheses involving only one variable. T PTS: 1 DIF: Easy REF: p. 507 OBJ: LO: 21-01 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 2. Multivariate statistic analyses require five or more variables. F Multivariate statistical analysis test hypotheses and models involving multiple (three or more) variables or sets of variables. PTS: 1 DIF: Moderate REF: p. 507 OBJ: LO: 21-01 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 3. The researcher’s hypothesis is generally stated in the form of a null hypothesis. F The researcher’s hypothesis is generally stated in the form of an alternative hypothesis. PTS: 1 DIF: Moderate REF: p. 508 OBJ: LO: 21-01 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 4. A statistical test’s significance level or p-value becomes a key indicator of whether or not a hypothesis can be supported. T PTS: 1 DIF: Moderate REF: p. 509 OBJ: LO: 21-02 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 5. A significance level is a critical probability associated with a statistical hypothesis test that indicates how likely it is that an inference supporting a difference between an observed value and some statistical expectation is true. T PTS: 1 DIF: Moderate REF: p. 509 OBJ: LO: 21-02 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 6. The term p-value stands for power-value. F It stands for probability-value. PTS: 1 DIF: Moderate REF: p. 509 OBJ: LO: 21-02 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 7. In hypothesis testing, the symbol typically used to specify the significance level of the test is . F It is . PTS: 1 DIF: Moderate REF: p. 510 OBJ: LO: 21-02 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 8. In hypothesis testing, the values of t that lie on the boundary of the region of rejection are called the critical values. T PTS: 1 DIF: Hard REF: p. 512 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 9. The researcher using sampling runs the risk of committing two types of errors: Type I and Type II errors. T PTS: 1 DIF: Moderate REF: p. 513 OBJ: LO: 21-04 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 10. A Type I error occurs when you fail to reject the null hypothesis when the alternative hypothesis is true. F A Type I error occurs when the researcher rejects the null hypothesis when it is true. PTS: 1 DIF: Moderate REF: p. 514 OBJ: LO: 21-04 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 11. A Type II error occurs when you reject the null hypothesis when, in fact, it is true. F This is a Type I error. A Type II error is caused by failing to reject the null hypothesis when the alternative hypothesis is true. PTS: 1 DIF: Moderate REF: p. 514 OBJ: LO: 21-04 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 12. In business problems, Type II errors generally are considered more serious than Type I errors. F Type I errors are considered more serious, and more emphasis is placed on determining the significance level, , than in determining . PTS: 1 DIF: Moderate REF: p. 515 OBJ: LO: 21-04 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 13. The scale of measurement used by the researcher determines the allowable statistical techniques in the research study. T PTS: 1 DIF: Moderate REF: p. 515 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 14. The two major groupings of statistical procedures are parametric statistics and nonparametric statistics. T PTS: 1 DIF: Moderate REF: p. 516 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 15. Nonparametric statistics are based on the assumption that the data in the study are drawn from a population with a normal (bell-shaped) distribution and/or normal sampling distribution. F This describes parametric statistics. PTS: 1 DIF: Moderate REF: p. 516 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 16. Nonparametric statistical tests are frequently referred to as distribution free. T PTS: 1 DIF: Hard REF: p. 516 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 17. Nominal scales typically use parametric statistical tests. F Data analysis of both nominal and ordinal scales typically uses nonparametric statistical tests. PTS: 1 DIF: Moderate REF: p. 516 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 18. A univariate t-test is appropriate for testing hypotheses involving some observed mean against some specified value. T PTS: 1 DIF: Moderate REF: p. 517 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 19. The t-test is strictly appropriate for tests involving sample sizes larger than 30 with known standard deviations. F The t-test is strictly appropriate for tests involving small sample sizes with unknown standard deviations. PTS: 1 DIF: Moderate REF: p. 517 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 20. Degrees of freedom are determined by the number of distinct calculations that are possible given a set of information. T PTS: 1 DIF: Moderate REF: p. 517 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 21. A two-tailed t-test is appropriate when the researcher has a directional hypothesis implying that an observed mean can only be greater than or less than a hypothesized value. F A one-tailed test is appropriate in this situation. A two-tailed test is one that tests for differences from the population mean that are either greater or less. PTS: 1 DIF: Moderate REF: p. 520 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 22. The logic behind the chi-square test is to compare the observed frequencies with the expected frequencies in the data set. T PTS: 1 DIF: Moderate REF: p. 521 OBJ: LO: 21-05 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 23. A t-test is appropriate for testing hypotheses about frequencies arranged in a frequency or contingency table. F A chi-square test is appropriate in this situation. PTS: 1 DIF: Moderate REF: p. 521 OBJ: LO: 21-05 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 24. The 2 distribution is a single probability curve. F The 2 distribution is not a single probability curve, but a family of curves that vary slightly with the degrees of freedom. PTS: 1 DIF: Hard REF: p. 523 OBJ: LO: 21-05 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 25. A hypothesis test of a proportion is conceptually similar to hypothesis testing when the mean is the characteristic of interest. T PTS: 1 DIF: Moderate REF: p. 524 OBJ: LO: 21-05 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension MULTIPLE CHOICE 1. Which type of statistical analysis test hypotheses involves only one variable? a. primary statistical analysis b. bivariate statistical analysis c. univariate statistical analysis d. monovariate statistical analysis C PTS: 1 DIF: Moderate REF: p. 507 OBJ: LO: 21-01 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 2. The opposite of the null hypothesis is called the ______ hypothesis. a. pure b. alpha c. alternative d. secondary C PTS: 1 DIF: Moderate REF: p. 508 OBJ: LO: 21-01 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 3. Which of the following is the key indicator of whether or not a hypothesis can be supported? a. critical value b. significance level c. chi-square d. degrees of freedom B PTS: 1 DIF: Moderate REF: p. 509 OBJ: LO: 21-02 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 4. Which of the following represents the acceptable Type I error? a. t-value b. 2 c. degrees of freedom d. significance level D PTS: 1 DIF: Moderate REF: p. 509 OBJ: LO: 21-02 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 5. A researcher is testing a hypothesis and is examining the data to determine whether or not the observed relationship between a salesperson’s age and sales are significantly related. Which of the following will he use to determine the significance level of the results? a. b. c. y-value d. p-value D PTS: 1 DIF: Hard REF: p. 509 OBJ: LO: 21-02 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Application 6. In statistical testing, the significance level is commonly denoted by the symbol _____. a. b. c. Zobs d. B PTS: 1 DIF: Moderate REF: p. 510 OBJ: LO: 21-02 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 7. The values that lie exactly on the boundary of the region of rejection for hypothesis-testing are called the _____. a. degrees of freedom b. critical values c. significance level d. confidence interval B PTS: 1 DIF: Moderate REF: p. 512 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 8. If the population mean is expected to be 85 and the sample mean is 80, the sample standard deviation is 20, and the sample consists of 100 consumers, the observed value of the Z-statistic is approximately _____. a. 2.50 b. -10.00 c. -2.50 d. -0.25 C PTS: 1 DIF: Hard REF: p. 513 OBJ: LO: 21-03 NAT: AACSB Analytic| CB&E Model Research| Blooms Application 9. The two types of errors researcher run the risk of committing when sampling are _____. a. primary and secondary errors b. Type I and Type II errors c. critical and noncritical errors d. Type A and Type B errors B PTS: 1 DIF: Moderate REF: p. 513 OBJ: LO: 21-04 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 10. The error caused by rejecting the null hypothesis when it is, in fact, true is called a _____. a. Type II error b. confidence level error c. confidence interval error d. Type I error D PTS: 1 DIF: Moderate REF: p. 514 OBJ: LO: 21-04 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 11. Which type of error occurs when the researcher concludes a relationship exists when in fact one does not exist? a. Type I b. Type II c. Type A d. Type B A PTS: 1 DIF: Moderate REF: p. 514 OBJ: LO: 21-04 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 12. When a researcher sets an acceptable significance level a priori (), he or she is determining how much tolerance he or she has for which type of error? a. Type I b. Type II c. Type A d. Type B A PTS: 1 DIF: Moderate REF: p. 514 OBJ: LO: 21-04 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 13. Failing to identify a hypothesized difference using a sample result when one really does exist in the population is which type of error? a. primary b. secondary c. Type I d. Type II D PTS: 1 DIF: Moderate REF: p. 514 OBJ: LO: 21-04 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 14. When the probability of a Type II error is ______ , the probability of a Type I error is _____. a. reduced, increased b. reduced; reduced c. increased; increased d. none of these choices A PTS: 1 DIF: Moderate REF: p. 515 OBJ: LO: 21-04 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 15. Selection of the appropriate statistical test to use in a research study depends on all of the following EXCEPT _____. a. the type of research question asked b. the number of variables c. the measurement scale used d. the statistical software used D PTS: 1 DIF: Hard REF: p. 515 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 16. Which type of statistics involves numbers with known, continuous distributions? a. Type I b. Type II c. parametric d. nonparametric C PTS: 1 DIF: Moderate REF: p. 516 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 17. When the data are in ______ form, and the sample size is ______ , the researcher should use parametric statistical procedures. a. nominal; large b. ordinal; large c. interval; large d. nominal; small C PTS: 1 DIF: Hard REF: p. 516 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 18. When a researcher wishes to analyze data that is nominal, which type of statistics is appropriate? a. Type I b. Type II c. parametric d. nonparametric D PTS: 1 DIF: Moderate REF: p. 516 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Comprehension 19. The t-distribution has a mean of ______ and a standard deviation of ______. a. one; zero b. zero; one c. one; two d. two; one B PTS: 1 DIF: Moderate REF: p. 517 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 20. When sample size (n) is larger than _____, the t-distribution and Z-distribution are almost identical. a. 10 b. 20 c. 25 d. 30 D PTS: 1 DIF: Hard REF: p. 517 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 21. The number of observations minus the number of constraints or assumptions needed to calculate a statistical term is called the _____. a. statistical power b. t-level c. degrees of freedom d. significance level C PTS: 1 DIF: Moderate REF: p. 517 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 22. For a one-group t-test, the degrees of freedom are _____. a. n 1 b. n(n 1) c. n 1 d. n(n 1) C PTS: 1 DIF: Hard REF: p. 517 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 23. Suppose that a group of 100 consumers are asked to rate how much they liked the taste of a new soft drink on a 5-point scale (where 5 = good taste and 1 = poor taste) and the mean rating was 4.2 with a standard deviation of 1.48. Suppose, further, that the standard error of the mean for this study was 0.15. If you wanted to find the 95 percent confidence interval (two-tailed test), and if the Z-value at the 0.05 level of significance is 1.96, the confidence interval lies between _____. a. 3.91 and 4.49 b. 4.17 and 4.23 c. 3.98 and 4.42 d. 4.00 and 5.00 A PTS: 1 DIF: Hard REF: p. 519 OBJ: LO: 21-03 NAT: AACSB Analytic| CB&E Model Research| Blooms Application 24. Which type of t-test is appropriate to test the following hypothesis? H: The number of employees who commute to work is greater than ten. a. Type I b. Type II c. one-tailed d. two-tailed C PTS: 1 DIF: Hard REF: p. 520 OBJ: LO: 21-03 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Application 25. Laura has a frequency table with the number of stores in three different categories: stand-alone, shopping center, and mall locations. Which statistical test is appropriate for testing hypothesizes she might have regarding these frequencies? a. test b. 2 test c. test d. test B PTS: 1 DIF: Hard REF: p. 521 OBJ: LO: 21-05 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Application 26. Which of the following represents how well some computed table or matrix of values matches some population or predetermined table or matrix of the same size? a. statistical power b. Z-value c. t-value d. goodness-of-fit (GOF) D PTS: 1 DIF: Moderate REF: p. 521 OBJ: LO: 21-05 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 27. For which statistical test does the formula given below apply? a. Z-test b. F-test c. Chi-square test d. W-square C PTS: 1 DIF: Hard REF: p. 522 OBJ: LO: 21-05 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge 28. In a brand awareness study of 80 consumers, 52 of them were able to identify "Fusion" as a type of Ford automobile. The chi-square value for a test of this brand awareness was approximately _____. a. 2.30 b. 7.20 c. 0.60 d. 3.60 B PTS: 1 DIF: Hard REF: p. 522 OBJ: LO: 21-05 NAT: AACSB Analytic| CB&E Model Research| Blooms Application 29. Suppose that past research studies have found that 70 percent of a particular target market segment were aware of the Nike "swoosh" brand mark. If 65 percent of this target market in a sample of 60 people are aware of this brand mark, and if the standard error of the proportion is 0.06, the observed Z-test value is approximately _____. a. -13.19 b. -0.83 c. 0.83 d. 13.19 B PTS: 1 DIF: Hard REF: p. 524 OBJ: LO: 21-05 NAT: AACSB Analytic| CB&E Model Research| Blooms Application 30. Which of the following tests is conceptually similar to the one used when the mean is the characteristic of interest but that differs in the mathematical formulation of the standard error of the proportion? a. hypothesis test of a proportion b. 2 test c. goodness of fit test d. degrees of freedom test A PTS: 1 DIF: Moderate REF: p. 524 OBJ: LO: 21-05 NAT: AACSB Reflective Thinking| CB&E Model Research| Blooms Knowledge COMPLETION 1. The type of statistical analysis that deals with a hypothesis about a single variable (e.g. market share) is called ______ statistical analysis. 2. Analyses that test hypotheses and models involving multiple (three or more) variables or sets of variables are referred to as _____ statistical analyses. 3. A statement which expresses the opposite of the null hypothesis is called the ______ hypothesis. 4. The critical probability associated with a statistical hypothesis test that indicates how likely it is that an inference supporting a difference between an observed value and some statistical expectation is true is called _____. 5. Another name for an observed or computed significance level is _____. 6. In hypothesis testing, the values that lie exactly on the boundary of the region of rejection are referred to as the ______ values. 7. The error caused by rejecting the null hypothesis when, in fact, it is true is called a(n) ______ error. 8. The error caused by failing to reject the null hypothesis when, in fact, the alternative hypothesis is true is called a(n) ______ error. 9. When the data are interval or ratio scaled and the sample size is large, _____ statistical procedures are appropriate. 10. When the researcher does not know how the data are distributed, the researcher should use ________ methods of statistics in analyzing the data. 11. The appropriate test to use when testing hypotheses involving an observed mean against some specified value is the univariate ______ . 12. The symmetrical, bell-shaped distribution that has a mean of zero and a standard deviation of one is called the ______. 13. In hypothesis testing, the number of observations minus the number of constraints needed to calculate a statistical term is called the ______. 14. The appropriate test for testing hypotheses about frequencies arranged in a frequency or contingency table is the _____ test. 15. A general term representing how well some computed table or matrix of values matches some population or predetermined table or matrix of the same size is _____. ESSAY 1. Explain the appropriate statistical analysis for the following hypothesis: H1: The average income of accountants is greater than $50,000. This is a univariate hypothesis dealing with one variable: income. Univariate hypotheses are typified by tests comparing some observed sample mean against a benchmark value. The test addresses the 2. Compare and contrast significance levels and p-values. A significance level is a critical probability associated with a statistical hypothesis test that indicates how likely it is that an inference supporting a difference between an observed value and some 3. Compare and contrast Type I errors and Type II errors and explain which one is of more concern to researchers. Hypothesis testing using sample observations is based on probability theory. Because we cannot make any statement about a sample with complete certainty, there is always the chance that an error will be made. The researcher using sampling runs the risk of committing two types of errors. A Type I error occurs when a condition that is true in the population is rejected based on statistical 4. You are designing a research study and are determining the appropriate statistical technique to use. List the factors you should consider when choosing the appropriate statistical technique. 5. Compare and contrast parametric statistics and nonparametric statistics. 6. Define one- and two-tailed univariate tests and describe when each is appropriate. Give an example hypothesis that can be tested with each test. 7. Describe the chi-square test for goodness-of-fit and explain when it is the appropriate test.