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Unit 4: Hypothesis Testing and Statistical Inferences - Practice Quiz

MGN206 — Research Methodology 60 Questions
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1 What is a hypothesis in research?

Concepts of Hypothesis Easy
A. A list of research references
B. A method for collecting data
C. A testable statement about variables
D. A final report of the study

2 What does the null hypothesis generally state?

Concepts of Hypothesis Easy
A. There is no significant effect or difference
B. The research result must be positive
C. The sample is larger than the population
D. There is always a strong relationship

3 What does the alternative hypothesis usually suggest?

Concepts of Hypothesis Easy
A. A significant effect or difference exists
B. The study has no research question
C. The variables have identical values
D. The data contain no observations

4 What is the main purpose of hypothesis testing?

Concepts of Hypothesis Easy
A. To replace data collection completely
B. To calculate only descriptive averages
C. To make decisions using sample evidence
D. To prove every research idea correct

5 Student's t-test is mainly used to compare:

Parametric Test - Student's t-test Easy
A. Means of one or two groups
B. Ranks across several groups
C. Frequencies across many categories
D. Variances of unrelated variables

6 Which situation is most suitable for an independent-samples t-test?

Parametric Test - Student's t-test Easy
A. Comparing ranks from three groups
B. Comparing means from two separate groups
C. Comparing one variance with another
D. Comparing counts in several categories

7 A paired-samples t-test is appropriate when:

Parametric Test - Student's t-test Easy
A. Three unrelated groups are measured once
B. Two population variances are compared
C. The same subjects are measured twice
D. Only category frequencies are recorded

8 Which statistic is commonly used in a t-test?

Parametric Test - Student's t-test Easy
A. The F-statistic
B. The t-statistic
C. The chi-square statistic
D. The rank-sum statistic

9 A Z-test is commonly used when the population standard deviation is:

Z-test Easy
A. Known
B. Always zero
C. Equal to the sample size
D. Never estimated

10 Which distribution is associated with the Z-test?

Z-test Easy
A. Standard normal distribution
B. F-distribution
C. Chi-square distribution
D. Student's t-distribution

11 A Z-test is generally suitable for testing a population mean when the sample is:

Z-test Easy
A. Large or normally distributed
B. Small and entirely categorical
C. Limited to two frequency tables
D. Made only of ranked observations

12 What does a Z-score indicate in a hypothesis test?

Z-test Easy
A. Distance from the mean in standard deviations
B. Difference between two sample variances
C. Total number of observations collected
D. Number of categories in a frequency table

13 The F-test is commonly used to compare:

F-test Easy
A. Two population medians
B. Two population variances
C. Two individual observations
D. Two category frequencies

14 Which distribution is used by the F-test?

F-test Easy
A. F-distribution
B. t-distribution
C. Normal distribution
D. Poisson distribution

15 In analysis of variance, the F-statistic compares:

F-test Easy
A. Sample size and population size
B. Observed and expected category counts
C. Two means from paired observations
D. Between-group and within-group variation

16 The chi-square test is primarily used with:

Nonparametric Test - Chi-Square Test Easy
A. Paired mean differences
B. Categorical frequency data
C. Known population variances
D. Continuous height measurements

17 What does a chi-square goodness-of-fit test compare?

Nonparametric Test - Chi-Square Test Easy
A. Observed and expected frequencies
B. Ranks across independent groups
C. Two population variances
D. Two sample means

18 A chi-square test of independence examines whether:

Nonparametric Test - Chi-Square Test Easy
A. Two means are significantly different
B. A sample mean equals a population mean
C. Several variances have the same value
D. Two categorical variables are related

19 The Kruskal-Wallis test is used to compare:

Kruskal-Wallis Test Easy
A. Three or more independent groups
B. Two population variances
C. Two paired measurements
D. One sample proportion

20 The Kruskal-Wallis test is a nonparametric alternative to:

Kruskal-Wallis Test Easy
A. A chi-square goodness-of-fit test
B. A paired t-test
C. One-way ANOVA
D. A Z-test for proportions

21 A study produces a p-value of while testing at the significance level. What is the appropriate decision?

Concepts of Hypothesis Medium
A. Accept the null hypothesis as true
B. Increase the significance level
C. Repeat the test with
D. Reject the null hypothesis

22 A researcher tests : a new drug has no effect. Which situation represents a Type I error?

Concepts of Hypothesis Medium
A. Concluding the drug fails when it works
B. Concluding the drug works when it does not
C. Concluding the drug fails when it does not
D. Concluding the drug works when it works

23 A manufacturer claims that the mean battery life is more than hours. Which pair of hypotheses is appropriate for testing this claim?

Concepts of Hypothesis Medium
A. ;
B. ;
C. ;
D. ;

24 A sample of students has a mean score of and a sample standard deviation of . To test , what is the one-sample t-statistic?

Parametric Test - Student's t-test Medium
A.
B.
C.
D.

25 Researchers record the blood pressure of the same patients before and after treatment. Which test is most appropriate for comparing the two mean readings?

Parametric Test - Student's t-test Medium
A. One-sample Z-test
B. Paired-samples t-test
C. Independent-samples t-test
D. Kruskal-Wallis test

26 Two independent samples contain and observations. If an equal-variance independent-samples t-test is used, what are its degrees of freedom?

Parametric Test - Student's t-test Medium
A.
B.
C.
D.

27 A random sample of observations comes from an approximately normal population whose variance is unknown. Which test should be used to test a claim about the population mean?

Parametric Test - Student's t-test Medium
A. F-test with degrees of freedom
B. Chi-square test with degrees of freedom
C. One-sample Z-test with degrees of freedom
D. One-sample t-test with degrees of freedom

28 A population has known standard deviation . A sample of observations has mean . For , what is the Z-statistic?

Z-test Medium
A.
B.
C.
D.

29 In a sample of voters, support a proposal. To test , what is the one-sample proportion Z-statistic?

Z-test Medium
A.
B.
C.
D.

30 Which situation is most suitable for a two-sample Z-test for the difference between means?

Z-test Medium
A. Two categorical variables summarized in a contingency table
B. Three independent samples measured on an ordinal scale
C. Two small paired samples with unknown population variances
D. Two large independent samples with known population variances

31 Two independent samples have variances and . If the larger variance is placed in the numerator, what is the calculated F-statistic?

F-test Medium
A.
B.
C.
D.

32 In a one-way ANOVA, the between-group mean square is and the within-group mean square is . What is the F-statistic?

F-test Medium
A.
B.
C.
D.

33 When an F-test is used to compare two population variances, which null hypothesis is tested?

F-test Medium
A.
B.
C.
D.

34 In a contingency table with total frequency , one row has a total of and one column has a total of . What is the expected frequency for their intersecting cell under independence?

Nonparametric Test - Chi-Square Test Medium
A.
B.
C.
D.

35 A chi-square test of independence uses a table with rows and columns. What are the degrees of freedom?

Nonparametric Test - Chi-Square Test Medium
A.
B.
C.
D.

36 A goodness-of-fit test has observed frequencies and expected frequencies . What is the chi-square statistic?

Nonparametric Test - Chi-Square Test Medium
A.
B.
C.
D.

37 Which condition most directly supports the usual chi-square approximation for a contingency table?

Nonparametric Test - Chi-Square Test Medium
A. Population means are normally distributed
B. Observed cell frequencies are all identical
C. Expected cell frequencies are generally at least
D. Population variances are exactly equal

38 A researcher compares satisfaction ratings on a five-point ordinal scale across four independent departments. Which test is most appropriate if normality cannot be assumed?

Kruskal-Wallis Test Medium
A. Chi-square goodness-of-fit test
B. Kruskal-Wallis test
C. One-sample Z-test
D. Paired-samples t-test

39 Three groups of two observations each have rank sums , , and . Ignoring tie corrections, what is the Kruskal-Wallis statistic?

Kruskal-Wallis Test Medium
A.
B.
C.
D.

40 A Kruskal-Wallis test comparing three independent groups gives . At , what is the appropriate conclusion?

Kruskal-Wallis Test Medium
A. Only the largest group differs significantly
B. All three group distributions are identical
C. Every pair of groups differs significantly
D. At least one group distribution differs

41 A researcher tests against and obtains a one-sided -value of . Which conclusion is logically valid at ?

Concepts of Hypothesis Hard
A. Reject and conclude that .
B. Accept and conclude that .
C. Accept because the null hypothesis includes .
D. Reject and conclude that the data support .

42 For a fixed one-sided test of against , which change generally decreases both the Type II error probability at a fixed alternative and the minimum detectable effect while keeping the Type I error rate unchanged?

Concepts of Hypothesis Hard
A. Replacing the one-sided alternative with a two-sided alternative
B. Decreasing the significance level while retaining the same sample size
C. Increasing the sample size while retaining the same significance level
D. Increasing the population variance while retaining the same sample size

43 Twenty independent null hypotheses are each tested at . If all null hypotheses are true, what is the familywise probability of at least one Type I error, assuming the tests are independent?

Concepts of Hypothesis Hard
A.
B.
C.
D.

44 For paired observations, the sample mean and standard deviation of the within-pair differences are and . For against , which conclusion is correct? Use and .

Parametric Test - Student's t-test Hard
A. Reject at both levels, because .
B. Reject at but not at , because .
C. Reject at but not at , because .
D. Reject at neither level, because .

45 Two independent normal samples have and . Under an equal-variance two-sample t-test of , what are the pooled variance and test statistic?

Parametric Test - Student's t-test Hard
A. and
B. and
C. and
D. and

46 In a two-sample comparison, group variances differ substantially and sample sizes are unequal. The observations are independent and approximately normal. Which procedure gives the most defensible test of ?

Parametric Test - Student's t-test Hard
A. A paired t-test using arbitrary cross-group pairings
B. A one-sample t-test applied to the combined observations
C. Welch's t-test with Satterthwaite degrees of freedom
D. The pooled t-test with degrees of freedom

47 A paired t-test is planned for before-and-after measurements. The marginal before and after distributions are skewed, but the distribution of paired differences is approximately normal with no severe outliers. Which statement is correct?

Parametric Test - Student's t-test Hard
A. The paired t-test remains appropriate because its normality condition concerns the differences.
B. The observations should be pooled because pairing is irrelevant under marginal skewness.
C. An independent-samples t-test is required because the marginal distributions are skewed.
D. The paired t-test is invalid because both marginal distributions must be exactly normal.

48 A normal population has known standard deviation . A sample of gives . For against , what are the test statistic and the decision at ?

Z-test Hard
A. ; fail to reject because
B. ; reject because
C. ; reject because
D. ; fail to reject because

49 In two independent samples, of observations in group 1 and of in group 2 are successes. For testing , what is the pooled two-proportion z statistic?

Z-test Hard
A. using
B. using
C. using
D. using

50 A one-sample proportion z-test of is proposed with , and the sample contains no successes. What is the main problem with relying on the usual normal approximation?

Z-test Hard
A. The observed proportion is zero, so a test statistic cannot be calculated.
B. The sample size exceeds the range for which a proportion z-test is valid.
C. The null expected success count is only , so the approximation may be poor.
D. The expected failure count is , so the variance under is zero.

51 Independent normal samples yield with and with . If the larger sample variance is placed in the numerator, which statistic and degrees of freedom are used to test equality of variances?

F-test Hard
A. with degrees of freedom
B. with degrees of freedom
C. with degrees of freedom
D. with degrees of freedom

52 For two groups, a standard equal-variance two-sample t-test produces with degrees of freedom. What F statistic would the equivalent one-way ANOVA produce?

F-test Hard
A. with degrees of freedom
B. with degrees of freedom
C. with degrees of freedom
D. with degrees of freedom

53 Two independent populations have equal variances but strongly right-skewed distributions with occasional extreme observations. Why can the classical F-test for equality of variances have a distorted Type I error rate?

F-test Hard
A. Its null distribution depends strongly on the populations being normal.
B. It requires the two sample means to be numerically identical.
C. It assumes that both population variances are known in advance.
D. Its statistic is unaffected by extreme observations but not by skewness.

54 A goodness-of-fit test has categories. Two parameters of the hypothesized distribution are estimated from the same data, and no categories are combined. What are the chi-square degrees of freedom?

Nonparametric Test - Chi-Square Test Hard
A.
B.
C.
D.

55 In a contingency table, one cell has observed count and expected count . What is that cell's contribution to Pearson's chi-square statistic?

Nonparametric Test - Chi-Square Test Hard
A.
B.
C.
D.

56 A table has expected counts in one row and in the other. What is the most defensible response before using the ordinary Pearson chi-square approximation?

Nonparametric Test - Chi-Square Test Hard
A. Replace expected counts by observed counts before calculating the statistic.
B. Proceed unchanged because the total sample size exceeds the number of cells.
C. Combine substantively compatible categories or use an exact alternative.
D. Delete cells with expected counts below five and retain the original degrees of freedom.

57 A Pearson chi-square test of independence on a table gives . What are the degrees of freedom, and what does rejection of independence establish?

Nonparametric Test - Chi-Square Test Hard
A. ; it establishes an association but not its causal direction.
B. ; it establishes that all cell residuals differ from zero.
C. ; it establishes that the row variable causes the column variable.
D. ; it establishes that every pair of categories is associated.

58 Three independent groups each contain observations. Their rank sums are , , and , with no ties. What is the Kruskal-Wallis statistic?

Kruskal-Wallis Test Hard
A.
B.
C.
D.

59 A Kruskal-Wallis test is significant for three independent groups whose distributions have markedly different shapes and spreads. Which interpretation is most defensible?

Kruskal-Wallis Test Hard
A. At least one population mean differs, while all population medians remain equal.
B. At least one group distribution differs, but the difference cannot be attributed solely to medians.
C. Every pair of population medians differs significantly from every other pair.
D. The group with the largest mean rank necessarily has the largest population mean.

60 A Kruskal-Wallis analysis has observations. One tied block contains observations and another contains ; all other ranks are untied. What tie-correction divisor should be applied to the uncorrected ?

Kruskal-Wallis Test Hard
A.
B.
C.
D.
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