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Chapter 21—Univariate Statistical Analysis TRUE/FALSE Monovariate statistical analysis tests hypotheses involving only one variable ANS: F These are called univariate statistical analyses PTS: REF: p 509 NAT: AACSB: Reflective Thinking The researcher’s hypothesis is generally stated in the form of a null hypothesis ANS: F The researcher’s hypothesis is generally stated in the form of an alternative hypothesis PTS: REF: p 510 NAT: AACSB: Reflective Thinking 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 ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 510 The term p-value stands for power-value ANS: F It stands for probability-value PTS: REF: p 510 NAT: AACSB: Reflective Thinking In hypothesis testing, the symbol typically used to specify the significance level of the test is ANS: F It is PTS: REF: p 511 NAT: AACSB: Reflective Thinking In hypothesis testing, the values of t that lie on the boundary of the region of rejection are called the critical values ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 513 The researcher using sampling runs the risk of committing two types of errors: primary errors and secondary errors ANS: F The two types of errors are Type I and Type II errors PTS: REF: p 515 NAT: AACSB: Reflective Thinking © 2010 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part 8 A Type I error occurs when you fail to reject the null hypothesis when the alternative hypothesis is true ANS: F A Type I error occurs when the researcher rejects the null hypothesis when it is true PTS: REF: p 515 NAT: AACSB: Reflective Thinking A Type II error occurs when you reject the null hypothesis when, in fact, it is true ANS: 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: REF: p 515 NAT: AACSB: Reflective Thinking 10 You have not made a mistake if the null hypothesis is false, and you decide to reject the null hypothesis ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 515 11 The scale of measurement used by the researcher determines the allowable statistical techniques in the research study ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 517 12 The two major groupings of statistical procedures are parametric statistics and nonparametric statistics ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 517 13 Parametric 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 ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 517 14 Nonparametric statistical tests are frequently referred to as "distribution free." ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 518 15 Nominal scales typically use parametric statistical tests ANS: F Data analysis of both nominal and ordinal scales typically uses nonparametric statistical tests PTS: REF: p 518 NAT: AACSB: Reflective Thinking 16 A univariate p-test is appropriate for testing hypotheses involving some observed mean against some specified value © 2010 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part ANS: F This is a t-test PTS: REF: p 518 NAT: AACSB: Reflective Thinking 17 The t-test is strictly appropriate for tests involving small sample sizes with unknown standard deviations ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 518 18 Degrees of freedom are determined by the number of distinct calculations that are possible given a set of information ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 519 19 The logic behind the chi-square test is to compare the observed frequencies with the expected frequencies in the data set ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 522 20 A hypothesis test of a proportion is conceptually similar to hypothesis testing when the mean is the characteristic of interest ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 525 MULTIPLE CHOICE 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 ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 509 The opposite of the null hypothesis is called the _ hypothesis a pure b alpha c alternative d secondary ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 510 Which of the following becomes key indicator of whether or not a hypothesis can be supported? a critical value b significance level c chi-square © 2010 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part d degrees of freedom ANS: B PTS: NAT: AACSB: Reflective Thinking REF: p 510 Alan is testing a hypothesis and is examining the data to determine whether or not the observed relationship between background music in a store 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 ANS: D PTS: NAT: AACSB: Reflective Thinking REF: p 510 In statistical testing, the significance level is commonly denoted by the symbol: a b c Zobs d ANS: B PTS: NAT: AACSB: Reflective Thinking REF: p 511 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 ANS: B PTS: NAT: AACSB: Reflective Thinking REF: p 514 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 ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 515 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 ANS: B PTS: NAT: AACSB: Reflective Thinking REF: p 515 The error caused by rejecting the null hypothesis when it is, in fact, true is called a: © 2010 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part a b c d Type II error confidence level error confidence interval error Type I error ANS: D PTS: NAT: AACSB: Reflective Thinking REF: p 515 10 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 ANS: A PTS: NAT: AACSB: Reflective Thinking REF: p 515 11 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 ANS: A PTS: NAT: AACSB: Reflective Thinking REF: p 515 12 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 ANS: D PTS: NAT: AACSB: Reflective Thinking REF: p 515 13 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 the above ANS: A PTS: NAT: AACSB: Reflective Thinking REF: p 516 14 Selection of the appropriate statistical test to use in a research study depends on: a the type of research question asked b the number of variables c the measurement scale used d all of the above ANS: D PTS: NAT: AACSB: Reflective Thinking REF: p 516 © 2010 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part 15 Which type of statistics involves numbers with known, continuous distributions? a Type I b Type II c parametric d nonparametric ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 517 16 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 ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 517 17 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 ANS: D PTS: NAT: AACSB: Reflective Thinking REF: p 518 18 The t-distribution has a mean of _ and a standard deviation of _ a one; zero b zero; one c one; two d two; one ANS: B PTS: NAT: AACSB: Reflective Thinking REF: p 518 19 When sample size (n) is larger than _, the t-distribution and Z-distribution are almost identical a 10 b 20 c 25 d 30 ANS: D PTS: NAT: AACSB: Reflective Thinking REF: p 518 20 The number of observations minus the number of constraints or assumptions needed to calculate a statistical term is called: a statistical power b t-level c degrees of freedom d significance level ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 519 © 2010 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part 21 For a one-group t-test, the degrees of freedom are: a n + b n(n 1) c n d n(n + 1) ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 519 22 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 = good taste and = 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 ANS: A PTS: NAT: AACSB: Reflective Thinking REF: p 520 23 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 ANS: B PTS: NAT: AACSB: Reflective Thinking REF: p 522 24 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) ANS: D PTS: NAT: AACSB: Reflective Thinking REF: p 522 25 For which statistical test does the formula given below apply? a b c d Z-test F-test Chi-square test W-square © 2010 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 523 26 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 ANS: B PTS: NAT: AACSB: Reflective Thinking REF: p 523 27 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 Ztest value is approximately: a -13.19 b -0.83 c 0.83 d 13.19 ANS: B PTS: NAT: AACSB: Reflective Thinking REF: p 525 COMPLETION The type of statistical analysis that deals with a hypothesis about a single variable (e.g market share) is called statistical analysis ANS: univariate PTS: REF: p 509 NAT: AACSB: Reflective Thinking Analyses that test hypotheses and models involving multiple (three or more) variables or sets of variables are referred to as statistical analyses ANS: multivariate PTS: REF: p 509 NAT: AACSB: Reflective Thinking A statement which expresses the opposite of the null hypothesis is called the hypothesis ANS: alternative PTS: REF: p 510 NAT: AACSB: Reflective Thinking 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 ANS: significance level © 2010 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part PTS: REF: p 510 NAT: AACSB: Reflective Thinking Another name for an observed or computed significance level is ANS: p-value PTS: REF: p 510 NAT: AACSB: Reflective Thinking In hypothesis testing, the values that lie exactly on the boundary of the region of rejection are referred to as the values ANS: critical PTS: REF: p 513 NAT: AACSB: Reflective Thinking The error caused by rejecting the null hypothesis when, in fact, it is true is called a(n) error ANS: Type I PTS: REF: p 515 NAT: AACSB: Reflective Thinking The error caused by failing to reject the null hypothesis when, in fact, the alternative hypothesis is true is called a(n) error ANS: Type II PTS: REF: p 515 NAT: AACSB: Reflective Thinking When the data are interval or ratio scaled and the sample size is large, statistical procedures are appropriate ANS: parametric PTS: REF: p 517 NAT: AACSB: Reflective Thinking 10 When the researcher does not know how the data are distributed, the researcher should use methods of statistics in analyzing the data ANS: nonparametric PTS: REF: p 517 NAT: AACSB: Reflective Thinking 11 The symmetrical, bell-shaped distribution that has a mean of zero and a standard deviation of one is called the ANS: t-distribution PTS: REF: p 518 NAT: AACSB: Reflective Thinking 12 The appropriate test to use when testing hypotheses involving an observed mean against some specified value is the univariate ANS: t-test © 2010 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part PTS: REF: p 518 NAT: AACSB: Reflective Thinking 13 In hypothesis testing, the number of observations minus the number of constraints needed to calculate a statistical term is called the ANS: degrees of freedom PTS: REF: p 519 NAT: AACSB: Reflective Thinking 14 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 ANS: goodness-of-fit PTS: REF: p 522 NAT: AACSB: Reflective Thinking ESSAY Explain the appropriate statistical analysis for the following hypothesis: H1: The average household income in zip code 71227 is greater than $50,000 ANS: 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 question, is the sample mean truly different from the benchmark? The level of scale measurement is ratio scaled, and if the sample size is large, parametric statistical procedures are appropriate In this case, a univariate t-test is appropriate for testing this hypothesis because in involves an observed mean income against the value of $50,000 PTS: REF: pp 509 NAT: AACSB: Reflective Thinking| AACSB: Communication Compare and contrast Type I errors and Type II errors and explain which one is of more concern to researchers ANS: 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 observations When a researcher sets an acceptable significance level a priori (), he or she is determining how much tolerance he or she has for a Type I error When testing for relationships, a Type I error occurs when the researcher concludes a relationship exists when in fact one does not exist A Type II error is the probability of failing to reject a false null hypothesis Alternatively, one can think of this as failing to identify a hypothesized difference using a sample result when one really does exist in the population This incorrect decision is called beta (), Type I errors generally are considered more serious than Type II errors Thus, more emphasis is placed on determining the significance level, , than in determining PTS: REF: p 515 © 2010 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part NAT: AACSB: Reflective Thinking| AACSB: Communication List the factors to consider when choosing the appropriate statistical technique ANS: Making the correct choice can be determined by considering the following points: (1) The type of question to be addressed (2) The number of variables involved (3) The level of scale measurement involved in each variable PTS: REF: p 516 NAT: AACSB: Reflective Thinking| AACSB: Communication Compare and contrast parametric statistics and nonparametric statistics ANS: The terms parametric statistics and nonparametric statistics refer to the two major groupings of statistical procedures The major distinction between them lies in the underlying assumptions about the data to be analyzed Parametric statistics involve numbers with known, continuous distributions When the data are interval or ratio and the sample size is large, parametric statistical procedures are appropriate Nonparametric statistics are appropriate when the numbers not conform to a known distribution Making the assumption that the population distribution or sampling distribution is normal generally is inappropriate when data are either ordinal or nominal Thus, nonparametric statistics are referred to as distribution free Data analysis of both nominal and ordinal scales typically uses nonparametric statistical tests PTS: REF: p 517 NAT: AACSB: Reflective Thinking| AACSB: Communication Describe the chi-square test for goodness-of-fit and explain when it is the appropriate test ANS: A chi-square ( 2) test is one of the most basic tests for statistical significance and is particularly appropriate for testing hypotheses about frequencies arranged in a frequency or contingency table Univariate tests involving nominal or ordinal variables are examined with a 2 More generally, this test is associated with goodness-of-fit (GOF) GOF can be thought of as how well some matrix (table) of numbers matches or fits another matrix of the same size Most often, the test is between a table of observed frequency counts and another table of expected values (central tendency) for those counts A chi-square test is the appropriate way for testing whether the values in a one-way frequency table are different than would be expected by chance PTS: REF: p 522 NAT: AACSB: Reflective Thinking| AACSB: Communication © 2010 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part ... 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 ANS: B PTS: NAT: AACSB: Reflective... AACSB: Reflective Thinking REF: p 522 25 For which statistical test does the formula given below apply? a b c d Z -test F -test Chi-square test W-square © 2010 Cengage Learning All Rights Reserved May... scales typically uses nonparametric statistical tests PTS: REF: p 518 NAT: AACSB: Reflective Thinking 16 A univariate p -test is appropriate for testing hypotheses involving some observed mean
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