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Chapter 16: Statistical Testing of Differences and
Relationships
Multiple Choice
1. Suppose in our sample results we find that males average drinking five soft drinks
per week, compared with six soft drinks per week for females. In the absence of
additional analysis, what type of difference has been illustrated?
a. statistical difference
b. managerially important difference
c. a difference of dispersion
d. mathematical difference
e. none of the above
2. What is the purpose of statistical inferences?
a. to fully describe the characteristics of the population
b. to make generalizations about population characteristics from sample
results
c. to estimate mean, median, mode, variance, and skewness of large sample
data
d. to study characteristics of binomial or Poisson random variables
e. all of the above
3. When do you say the difference between two numbers is statistically significant?
a. as long as the two numbers are not exactly the same
b. if the difference is large enough so that it is managerially important
c. if the difference is mathematically different
d. if the difference is observed over an extended period of time
e. if the difference is large enough to be unlikely to have occurred because of
chance or sampling error
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4. In a beer consumption study, a researcher makes an assumption that males will
consume more beer per week than females; this can be stated in a:
a. research objective.
b. given level of significance.
c. hypothesis.
d. theory.
e. rule.
5. What is the purpose of hypothesis testing?
a. to draw conclusive decisions about sample estimates
b. to determine whether there is support to draw conclusions about some
characteristics of the population given the evidence provided by the
sample results
c. to summarize and describe the sample data
d. to test whether the sample is scientifically drawn from a target population
e. to conduct statistical tests on census data
6. Which of the following is not a step in hypothesis testing?
a. evaluating the randomness of the sample
b. stating null and alternative hypotheses
c. choosing the appropriate statistical test
d. developing a decision rule given the significance level
e. All of the above are steps in hypothesis testing.
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7. The hypothesis of the status quo is typically referred to as the ______________
hypothesis.
a. type III
b. alternative
c. statistical
d. null
8. Which of the following is the appropriate statistical test when examining cross
tabulations?
a. chi-square test
b. t-test
c. z-test
d. one-way ANOVA
e. none of the above
9. What is the typical (rule of thumb) alpha level used in hypothesis testing?
a. .02
b. .05
c. .10
d. none of the above
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10. In testing a hypothesis about means, if the sample size was less than 30, then the
appropriate statistical test would be?
a. chi-square test
b. t-test
c. z-test
d. one-way ANOVA
e. none of the above
11. In most statistical software packages, the t-test is often substituted for which test
statistic?
a. chi-square test
b. f-test
c. z-test
d. one-way ANOVA
f. none of the above
12. The exact probability of getting a computed test statistic that was largely due to
chance is referred to as the______________.
a. p-value
b. chi-square value
c. z-test value
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d. median value
f. none of the above
13. For comparing means, most statistical software packages use which test?
a. chi-square
b. anova
c. t-test
d. beta
14. What is the meaning of testing a hypothesis at an alpha level of 0.05?
a. There is 95% confidence that the observed results are due to sampling
error or because of sample randomness.
b. The chances of not rejecting the null hypothesis when it is false is more
than 5%.
c. There is a 95% chance that the observed result from the sample analysis
will also occur in the population.
d. The probability of committing a Type II error is about 5%.
e. There is 95% chance of a gamma error.
15. What kind of error is being made if the researcher fails to reject the null
hypothesis when it is, in fact, false?
a. chi-square
b. type I
c. type II
d. type III
e. none of the above
16. Why is the null hypothesis called the hypothesis of the status quo?
a. It is the hypothesis that will not be rejected, unless the data provide
convincing evidence that it is false, thus maintaining the status quo.
b. It is not the research claim being tested.
c. It is the hypothesis that recommends the method of analysis.
d. The alternative hypothesis is operational only in the event of a Type II
error.
e. all of the above
17. Which of the following is the first step in hypothesis testing?
a. calculating the value of the test statistic
b. stating the hypothesis
c. choosing the appropriate test statistic
d. stating the conclusion
f. developing a decision rule
18. A researcher is interested in comparing product rating scores between males and
females. By drawing a sample of males and a sample of females, the researcher
needs to find a statistical test that applies to____________.
a. independent samples
b. dependent samples
c. convenience samples
d. none of the above
19. Samples in which the measurement of a variable in one population may influence
the measurement of the variable in the other are called:
a. stratified samples.
b. dependent samples.
c. related samples.
d. constrained samples.
f. nonprobability samples.
20. What type of data would be necessary to have when testing for differences in
means?
a. nominal
b. ordinal
c. metric
d. none of the above
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21. A market researcher is trying to determine whether males differ from females
with regard to the following question: Do you drink soft drinks? Which of the
following tests would be most appropriate?
a. chi-square test
b. 1-way AVOVA test
c. correlation analysis
d. median test
e. Kolmogorov-Smirnov Test
22. Hypotheses about frequency distributions that involve one or more nominally
scaled variables can be tested using ____________.
a. chi-square test
b. t-test
c. f-test
d. z-test
e. ANOVA test
23. What determines the decision of whether to use a one-tailed test or a two-tailed
test when testing hypotheses to make inferences about a population mean?
a. the sample size and the estimated standard error
b. the nature of the situation and what the researcher is trying to demonstrate
c. the level of significance of the test
d. the sample size relative to the population size
e. the standard error relative to the sample variance
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Ans: B
Difficulty: Hard
Response: See page 478
Ref: Hypothesis Testing
Learning Objective 16.2: To understand the concept of hypothesis development and
how to test hypotheses.
24. The number of observations minus the number of assumptions necessary to
calculate a statistic equals:
a. the Z score.
b. ANOVA.
c. random variation.
d. degrees of freedom.
25. Researchers must be careful to distinguish statistical significance from:
a. mathematical significance.
b. chance significance.
c. practical significance.
d. random significance.
26. Hypotheses are stated in two basic forms: __________ & _____________.
a. Null & Fake
b. Null & Real
c. Null & Alternative
d. Alternative & Real
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Ref: Hypothesis Testing
Learning Objective 16.2: To understand the concept of hypothesis development and
how to test hypotheses.
27. A(n) ________________ is a standard used to determine whether to reject or fail
to reject the null hypothesis.
a. Decision rule
b. Common rule
c. Determined rule
d. Assessment rule
28. A(n) ____ test is a test of the probability that a particular calculated value could
have been due to chance.
a. P
b. Z
c. T
d. F
True/False
29. In marketing research, the basic motive for making statistical inferences is to
generalize from sample results to population characteristics.
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30. An assumption or theory that a researcher or manager makes about some
characteristic of the population under study is an inference.
31. The last step in testing a hypothesis is the development of a decision rule.
32. In testing a hypothesis from a random sample involving three or more means, the
appropriate test would be a one-way ANOVA.
33. When testing hypotheses about frequency distributions, nominal variables are
acceptable.
34. In related samples, the measurement of the variable of interest has no influence on
the measurement of the variable in another sample.
35. The z-test would be appropriate for testing three or more proportions when the
sample size is less than 30.
36. Mathematical differences are the same as statistically significant differences.
37. If a particular difference is large enough to be unlikely to have occurred because
of chance or sampling error, then the difference is statistically significant.
38. A Type I error involves rejecting the null hypothesis when it is, in fact, true.
39. The chi-square test enables the research analyst to determine whether an observed
pattern of frequencies corresponds to, or fits, an “unexpected pattern.”
40. The smaller the p value, the smaller is the probability that the observed result
occurred by chance.
41. A p value of .285 would be acceptable for a research analyst to reject the null
hypothesis.
42. ANOVA is used to analyze the differences of more than 2 means.
43. If the alternative hypothesis is supported, the researcher concludes there are
significant differences in the phenomenon being measured.
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Difficulty: Medium
Response: See page 485
Ref: Hypothesis Testing
Learning Objective 16.2: To understand the concept of hypothesis development and
how to test hypotheses.
44. There are fewer statistics available for analyzing nominal data than there are for
analyzing metric data.
45. Researchers cannot perform statistical testing on nominal data.
46. Researchers cannot perform statistical testing unless the sample size is at least 30.
47. Failing to reject the null hypothesis is the same as accepting the null hypothesis.
48. Researchers very rarely know the population mean.
49. The issue of whether certain measurements are different from one another is
central to many questions of critical interest to marketing managers.
50. In the decision that the null hypothesis is accepted, there must be enough evidence
in the data that the alternative hypothesis is correct.
51. The hypothesis test of proportions is a test to determine whether the difference
between two proportions is greater than would be expected because of sampling
error.
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52. ANOVA is a statistical technique that permits the researcher to determine whether
the variability among or across the independent sample means is greater than
expected because of sampling error.
Essay Questions
53. A consultant has a random sample of 400 usable responses in a database.
Included are the following questions:
Household Income Category:
(1) $0 to $24,999 (2) $25,000 to $49,999 (3) $50,000 to $99,999
(4) $100,000 and over
Average Weekly Soft Drink Consumption: _______________________
The consultant wants to determine if there are any statistically significant
differences in average weekly soft drink consumption by income category. What
statistical test should be applied to give the consultant the information he needs?
54. A consultant has collected 700 usable responses via a probability sample
concerning political opinions. After analyzing each respondent’s political
ideology, he/she divides the respondents into two groups, moderate liberals and
moderate conservatives. Further, the consultant asks respondents the following:
How likely are you to vote for increasing property taxes in the next election?
(1) very unlikely (2) somewhat unlikely (3) undecided
(4) somewhat likely (5) very likely
The consultant wants to determine if the moderate conservatives differ
significantly from moderate liberals concerning how they’ll vote on the property
tax issue in the next election. How should the data be analyzed?
55. The ANOVA technique requires two pieces of information from the researcher.
Describe these two pieces of information and the level of measurement associated
with each.
56. Suppose a client wants to evaluate average weekly miles jogging by males and
females. Initially, the consultant thinks a t-test would be the preferred method of
analysis. However, the client wants to know where the differences exist among
short, medium and long mileage joggers. What will the consultant have to do to
satisfy his/her client?
57. Illustrate a situation when is it more appropriate to use an Anova test rather than a
crosstabulation with the chi-square test.