BA5106
STATISTICS FOR MANAGEMENT
UNIT-IV- NON-PARAMETRIC TESTS
MULTI CHOICE QUESTIONS
1. The degrees of freedom for the Chi-Square test statistic when testing for independence in a contingency table with 4 rows and 4 columns would be
(A) 5
(B) 7
(C) 12
(D) 9}
2. The null hypothesis for the Chi-Square test of independence should specify
(A) that the two categorical variables are independent
(B) that the two numerical variables are dependent
(C) that the two categorical variables are dependent
(D) that the two numerical variables are independent
3.Which of the following values of the Chi-Square test statistic would be most likely to suggest that the null hypothesis were really true?
(A) 23.7183
(B) 0.3251
(C) 14.9728
(D) 18.3445
4.Which of the following values of the chi-square distribution cannot occur
(A) 0.61
(B) 38.4
(C) -2.45
(D) 100
5.The chi-square test can be used:
(A) for pairwise multiple comparisons of means
(B) to make inference about a population mean.
(C) to test for homogeneity of proportions.
(D) to test for difference in two variances.
6.To determine whether a set of observed frequencies differ from their corresponding expected frequencies, we could apply the
(A) chi-square test
(B) F test
(C) t test dependent samples
(D) t test independent samples
7. When using the chi-square test for differences in two proportions with a contingency table that has r rows and c columns, the degrees of freedom for the test statistic will be
(A) $n_1+n_2-1$
(B) (r-1)(c-1)
(C) n-1
(D) (r-1)+(c-1)
8. An alternative approach to utilizing the chi-square test for equality of c proportions would be to use the
(A) z-test for proportions
(B) one-way ANOVA
(C) chi-square test for independence
(D) t-test
9. What is the mean of a Chi Square distribution with 6 degrees of freedom?
(A) 4
(B) 12
(C) 8
(D) 6
10.Which Chi Square distribution looks the most like a normal distribution
(A) A Chi Square distribution with 4 degrees of freedom
(B) A Chi Square distribution with 5 degrees of freedom
(C) A Chi Square distribution with 6 degrees of freedom
(D) A Chi Square distribution with 16 degrees of freedom
11. The Mean of Chi Squared distribution is given as k. The Variance of Chi Squared distribution is ________
(A) 2+k
(B) k
(C) 2k
(D) 2-k
12. The null hypothesis in the chi-square test states that
(A) The rows and columns in the table are associated
(B) Neither of the two
(C) The rows in table are associated
(D) The rows and columns in the table are not associated
13. What is the formula used to calculate the $\chi^2$ statistic?
(A) $\sum \frac{(O-E)^2}{E}$
(B) $\sum \frac{(O+E)^2}{E}$
(C) $\sum \frac{(O\times E)^2}{E}$
(D) $\sum \frac{(O-E)^2}{E^2}$
14. What symbol is used to represent chi-square?
(A) $\phi$
(B) $\chi^2$
(C) n
(D) F
15.What is an effect size?
(A) The number of expected cases
(B) The chi-square value
(C) The variance explained by the measures
(D) The magnitude of the relationship between variables
16. Which of the following statement regarding the chi-square distribution is false?
(A) The chi square goodness of fit always one sided
(B) The degree of freedom for a test of association is (r-1)(c-1) in contingency table with r rows and c columns
(C) The chi square distribution is very skew to the left
(D) The chi square distribution can be used to test for normality
17. The major difference between the chi-square test of homogeneity and the chi-square test of independence is the
(A) number of categories
(B) sample size
(C) . size of the $\chi^2$ statistic
(D) Method of sampling
18.The null hypothesis is rejected in a chi-square test of significance when
(A) The test conditions are satisfied
(B) The $\chi^2$ statistic is larger than the critical value for the given level of significance
(C) The P-value is larger than $1-\alpha$
(D) The P-value is larger than $\alpha$ the level of significance
19. Which is the following is the explanatory variable in this study
(A) Occupation
(B) Lung capacity
(C) Smoking or not
(D) Exercise
20. Which is the following is the confounding variable in this study
(A) Lung capacity
(B) Exercise
(C) Smoking or not
(D) Occupation
21. The sign test assumes that the samples are
(A) Independent
(B) Dependent
(C) Have the same mean
(D) None of these
22.
Comparing the times-to-failure of radar transponders made by firms A,
B, and C, based on an airline’s sample experience with the three types
of instruments, one may well call for:
(A) A Kolmogorov-Smirnove test
(B) A Wilcoxon rank-sum test
(C) A Spearman rank-correlation test
(D) A Kruskal-Wallis test
23. In a Wilcox on rank-sum test
(A) Ties never affect the decision
(B) Ties within one sample may affect the decision
(C) Ties between the two samples may affect the decision
(D) Ties always affect the decision
24.The non parametric equivalent of an unpaired samples t-test is
(A) Sign test
(B) Wilcoxon signed-rank test
(C) Mann-Whitney U test
(D) Kruskal-Wallis test
25.
Which of the following test is most likely assessing the null
hypothesis of “the number of violations per apartment in the population
of all city apartments is binomial distributed with a probability of
success in any one trial of P=0.4”
(A) The Kolmogorov-Smirnove test
(B) The Kruskal-Wallis test
(C) The Mann-Whitney test
(D) The Wilcoxon signed-rank test
26. The Spearman rank-correlation test requires that the
(A) Data must be measured on the same scale
(B) Data at least ordinal scale
(C) Data must be from two independent samples
(D) Data must be distributed at least approximately as a t-distribution
27.Three
brands of coffee are rated for taste on a scale of 1 to 10. Six persons
are asked to rate each brand so that there is a total of 18
observations. The appropriate test to determine if three brands taste
equally good is
(A) Kruskal-Wallis test
(B) One way analysis of variance
(C) Wilcoxon rank-sum test
(D) Spearman rank difference
28.To perform a runs test for randomness the data must be
(A) Divided into at least two classifications
(B) Divided into exactly two classifications
(C) Quantitative
(D) Qualitative
29. In testing for the difference between two populations, it is possible to use
(A) The Wilcoxon rank-sum test
(B) The sign test
(C) Either of the above
(D) None of the these
30. If a Chi-square goodness of fit test has 6 categories and an N=30, then the correct number of degrees of freedom is
(A) 4
(B) 5
(C) 28
(D) 29
31. The sign test is
(A) More powerful than the pared sample t-test
(B) More powerful than the Wilcox on signed-rank test
(C) Less powerful than that of the Wilcox on signed-rank test
(D) Equivalent to the Mann-Whitney test
32.The Wilcox on rank-sum test can be
(A) Upper tailed
(B) Lower tailed
(C) Either of upper tailed or lower tailed
(D) None of these
33. The Runs test results in rejecting the null hypothesis of randomness when
(A) There is an unusually large number of runs
(B) There is an unusually small number of runs
(C) Either of the above
(D) None of these
34. The Wilcoxon signed-rank is used
(A) Only in matched pairs samples
(B) Only with independent samples
(C) As an alternative to the Kruskal-Wallis test
(D) To test for randomness
35. The Mann-Whitney U test is preferred to a t-test when
(A) Data are paired
(B) The assumption of normality is not met
(C) Sample sizes are small
(D) Samples are dependent
36. When testing for randomness, we can use
(A) Mann-Whitney U test
(B) Runs test
(C) Sign test
(D) None of these
37. Compare to parametric methods, the non parametric methods are
(A) Less accurate
(B) Less efficient
(C) Computationally easier
(D) (b) and (c) but not (a)
38. Which of the following test use rank sums?
(A) F test
(B) Kruskal-Wallis and Wilcox on test
(C) Chi-square and Sign tests
(D) Runs test
39 .When using the Sign test, if two scores are tied, then we
(A) Count them
(B) Depends upon the scores
(C) Discard them
(D) None of these
40. The Wilcox on rank-sum test compares
(A) Two populations
(B) Three or more populations
(C) A sample mean to the population mean
(D) None of these
41. In the Krystal-Wallis test of $k$ samples, the appropriate number of degrees of freedom is
(A) $ K $
(B) ${}^nC_{k} $
(C) $ K-1 $
(D) $ n-K $
42. Which of the following tests must be two-sided?
(A) Krystal-Wallis test
(B) Sign test
(C) Wilcox on Signed rank test
(D) Runs test
43.
A collection of statistical methods that generally requires very few,
if any assumptions about the population distribution is known as
(A) non-parametric methods
(B) parametric methods
(C) semi parametric
(D) none of the above
44.Which of the following tests would be an example of a non-parametric method?
(A) Z-test
(B) t-test
(C) sign test
(D) all of the above
45. A non parametric version of the parametric analysis of variance test is
(A) sign-test
(B) Mann-Whitney-Wilcox on Test
(C) Wilcox on Signed-rank test
(D) Kruskal-Wallis Test
46.
A non parametric method for determining the differences between two
populations based on two matched samples where only preference data is
required is the
(A) Krystal-Wallis Test
(B) Mann-Whitney-Wilcox on test
(C) Wilcox on signed-rank test
(D) sign test
47.When ranking combined data in a Wilcoxon signed rank test, the data that receives a rank of 1 is the
(A) highest value
(B) lowest value
(C) middle value
(D) This can vary according to data
48.The collection of statistical methods that require assumptions about the population is known as
(A) distribution free methods
(B) non-parametric methods
(C) parametric methods
(D) either a or b
49. The Spear man rank-correlation coefficient is
(A) X a correlation measure based on the average of data items
(B) a correlation measure based on rank-ordered data for two variable
(C) either a or b
(D) none of the above
50.The level of measurement that allows for the rank ordering of data items is
(A) nominal measurement
(B) ratio measurement
(C) interval measurement
(D) ordinal measurement
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