Deck 14: Analysis of Categorical Data

Question 1

The Wilcoxon rank sum test statistic "T" is approximately normally distributed whenever the sample sizes are larger than:

A)10
B)5
C)9
D)8

Answer 1

10

Question 2

Comparing the output of strawberries grown on plots using fertilizer A with that grown on otherwise identical plots using fertilizer B,in order to make a general assessment of relative fertilizer effectiveness,may well call for a:

A)Wilcoxon signed rank test.
B)Wilcoxon rank sum test.
C)Sign test.
D)Spearman rank correlation test.

Answer 2

Wilcoxon rank sum test.

Question 3

If for a particular data set,the skewness = -0.2,and the kurtosis equals 2.1,then it can be inferred that:

A)the data is skewed to the right and the distribution is less spread out than a normal distribution.
B)the data is skewed to the right and the distribution is more spread out than a normal distribution.
C)the data is skewed to the left and the distribution is more spread out than a normal distribution.
D)the data is skewed to the left and the distribution is less spread out than a normal distribution.

Answer 3

the data is skewed to the left and the distribution is less spread out than a normal distribution.

Question 4

A goodness-of-fit-test is to be performed to see if consumers prefer any of four package designs (A,B,C,andD)more than the other three.If a random sample of 60 consumers is selected,what is the expected frequency for category A?

A)0.25
B)30
C)15
D)10

Question 5

The Wilcoxon signed rank test assumes that the population distribution in the difference of paired samples:

A)follows a chi-square distribution.
B)follows a Poisson distribution.
C)follows a binomial distribution.
D)is symmetrical.

Question 6

For a chi-square goodness-of-fit-test,the calculated chi-square value is 7.21.If the table chi-square value is 10.645,what is the appropriate decision for this test?

A)Reject the null hypothesis.
B)Fail to reject the null hypothesis.
C)Accept both the null and the alternative hypothesis.
D)It is impossible to determine anything from the given information.

Question 7

Which of the following is not a reason to prefer a nonparametric test to a parametric test?

A)Nonparametric tests can be used for ordinal data.
B)Nonparametric tests are computationally more straightforward.
C)Nonparametric tests are less influenced by outliers.
D)Nonparametric tests are more powerful under conditions of normality.

Question 8

To apply the Wilcoxon rank sum test to determine whether the location of population 1 is different from the location of population 2,the:

A)samples must not be drawn randomly.
B)samples must be drawn from matched pairs of observations.
C)samples must be independent.
D)sample size must be larger than 30.

Question 9

A chi-square goodness-of-fit-test is being used to determine if the observed frequencies and the expected frequencies from six categories are significantly different.If no parameters are estimated from the data,what is the number of degrees of freedom for this test?

A)5
B)6
C)4
D)2

Question 10

A goodness-of-fit-test is always conducted as a(n):

A)lower-tail test.
B)upper-tail test.
C)asymmetric two-tailed test.
D)symmetric two-tailed test.

Question 11

A random sample of n observations,each of which could be classified into exactly one of k categories,is selected.How many degrees of freedom does a goodness-of-fit-test with specified probabilities have?

A)k-1
B)k-2
C)k-3
D)k +1

Question 12

Consider a cell in a contingency table.Given the cell's row total of 200 and a sample size of 1,000,the cell's expected frequency:

A)equals 0.5
B)equals 100
C)equals 200
D)cannot possibly be determined without additional information.

Question 13

Consider a chi-square distributed random variable with 12 degrees of freedom and a significance level of 0.025.The chi-square value from the table is 23.337.Which of the following computed values of the chi-square test statistic would lead us to a decision "fail to reject" the null hypothesis?

A)41.47
B)17.12
C)32.59
D)26.43

Question 14

If for a particular data set,the skewness = 0.42,and the kurtosis equals 3.85,then we know that:

A)the data is skewed to the left and the distribution is more spread out than a normal distribution.
B)the data is skewed to the right and the distribution is more spread out than a normal distribution.
C)the data is skewed to the left and the distribution is less spread out than a normal distribution.
D)the data is skewed to the right and the distribution in less spread out than a normal distribution.

Question 15

Suppose that for a random sample of 14 observations of random variables X and Y we compute a Spearman's rank correlation of 0.52.Is there sufficient evidence to reject the null hypothesis of no relationship between X and Y?

A)Reject H₀ at α = 0.10
B)Reject H₀ at α = 0.01
C)Reject H₀ at α = 0.025
D)Reject H₀ at α = 0.05

Question 16

The area to the right of a chi-square value is 0.025.For 5 degrees of freedom,the table value is:

A)12.83
B)15.08
C)11.14
D)16.18

Question 17

A chi-square test for independence with 8 degrees of freedom results in a test statistic of 18.21.Using the chi-square table,the most accurate statement that can be made about the p-value for this test is that:

A)p-value < 0.01
B)0)01< p-value < 0.025
C)0)025 < p-value < 0.05
D)0)05 < p-value < 0.10

Question 18

In a chi-square test of a contingency table,the value of the test statistic was χ² = 12.678,and the critical value at α = 0.025 was 14.4494.Thus:

A)we don't have enough evidence to accept or reject the null hypothesis at α = 0.025.
B)we should decrease the level of significance in order to reject the null hypothesis.
C)we fail to reject the null hypothesis at α = 0.025.
D)we reject the null hypothesis at α = 0.025.

Question 19

A chi-square test for independence with 10 degrees of freedom results in a test statistic of 18.21.Using the chi-square table,the most accurate statement that can be made about the p-value for this test is that:

A)0)01< p-value < 0.025
B)0)025 < p-value < 0.05
C)0)05 < p-value < 0.10
D)0)10 < p-value < 0.20

Question 20

Consider the following data set: 16,16,17,18,20,21,21,22,23,24,25,27,27,27,27,and 30.The rank assigned to the four observations of value 27 is:

A)13
B)13.5
C)12
D)12.5

Question 21

Which of the following refers to a nonparametric method to compare two populations,when the samples are independent and the data are either ordinal or interval,and where the normality requirement necessary to perform the parametric test is not satisfied?

A)Sign test
B)Wilcoxon signed rank test
C)Equal-variance t-test of μ₁ - μ₂
D)Wilcoxon rank sum test or Mann-Whitney test

Question 22

The number of degrees of freedom in a chi-square goodness-of-fit-test when population parameters are estimated is equal to the number of:

A)categories.
B)categories minus 1.
C)categories minus the number of parameters estimated.
D)categories minus the number of parameters estimated minus 1.

Question 23

In a goodness-of-fit-test,suppose that the value of the test statistic is 13.08 and degrees of freedom = 6.At the 5% significance level,the null hypothesis is:

A)rejected,and p-value for the test is smaller than 0.05.
B)not rejected,and p-value for the test is greater than 0.05.
C)rejected,and p-value for the test is greater than 0.05.
D)not rejected,and p-value for the test is smaller than 0.05.

Question 24

A chi-square goodness-of-fit-test is to be performed to see if data fit the Poisson distribution.There are 8 categories,and the parameter λ must be estimated.How many degrees of freedom should be used?

A)8
B)7
C)6
D)5

Question 25

A two-way table used for a test of independence is sometimes called a:

A)contingency table.
B)frequency table.
C)t table.
D)manifold table.

Question 26

Which of the following should certainly be known to select a value in the chi-square distribution table?

A)the mean and the variance of the observations
B)the level of significance and the variance of the observations
C)the degrees of freedom and the mean of the observations
D)the level of significance and the degrees of freedom

Question 27

A contingency table is to be used to test for independence.There are 3 rows and 3 columns in the table.How many degrees of freedom are associated with this test?

A)9
B)6
C)4
D)2

Question 28

Consider a cell in a contingency table.Given the cell's row total of 40,the cell's column total of 50,and a sample size of 250,the cell's expected frequency:

A)equals 8.
B)equals 5.
C)equals 40.
D)cannot possibly be determined without additional information.

Question 29

A chi-square goodness-of-fit-test is to be performed.If the degrees of freedom are 8,and α = 0.10,then the table chi-square value that defines the rejection region is:

A)13.362
B)15.507
C)17.535
D)12.017

Question 30

A test of independence is to be performed.The table has 4 rows and 5 columns.What would the degrees of freedom be?

A)20
B)15
C)12
D)9

Question 31

In a normal approximation to the Wilcoxon signed rank test,the test statistic is calculated as z = 1.26.For a two-tail test,the p-value is:

A)0.2076
B)0.3962
C)0.1238
D)0.3974

Question 32

A chi-square test of a contingency table with 4 rows and 5 columns shows that the value of the test statistic is 22.18.The most accurate statement that can be made about the p-value for this test is that the p-value is:

A)greater than 0.05 but smaller than 0.10.
B)smaller than 0.025.
C)greater than 0.025 but smaller than 0.05.
D)greater than 0.10.

Question 33

The significance level for a Wilcoxon signed rank test is 0.05.The alternative hypothesis is stated as: The location of population 1 is to the left of the location of population 2.The appropriate critical value for a sample of size 20 (that is the number of nonzero differences)is:

A)122
B)150
C)61
D)75

Question 34

Which of the following statements about nonparametric tests is false?

A)We can safely employ nonparametric tests even when we know nothing at all about the population from which sample data are being drawn.
B)We can conduct nonparametric tests with nominal data.
C)We can conduct nonparametric tests with ordinal data.
D)We can only conduct nonparametric tests with data of a higher order than nominal or ordinal.

Question 35

A chi-square goodness-of-fit-test is being used to determine if the observed frequencies and expected frequencies from five categories are significantly different.If only one parameter is estimated from the data,what is the critical chi-square value associated with α = 0.05?

A)3.84
B)5.99
C)7.81
D)9.49

Question 36

A test of independence is to be performed.The table has 4 rows and 3 columns.What would the degrees of freedom be?

A)12
B)6
C)9
D)3

Question 37

The nonparametric tests like the Sign test,the Wilcoxon rank sum test,the Mann-Whitney test,and the Wilcoxon signed rank test require that the probability distributions be:

A)identical except with respect to location.
B)identical except with respect to spread (variance).
C)identical except with respect to shape (distribution).
D)different with respect to location,spread,and shape.

Question 38

In the sign test for paired differences,the test statistic S has a:

A)binomial distribution with P = 0.5.
B)normal distribution.
C)chi-square distribution.
D)Poisson distribution.

Question 39

For a random sample of 247 observations,the skewness of the data was calculated to be -0.52 while the kurtosis was calculated to be 3.24.Which of the following is true in the light of the information given above?

A)Reject H₀ for α = 0.05,but not for α = 0.10
B)Reject H₀ for α = 0.10,but not for α = 0.5
C)Reject H₀ for α= 0.05 and for α = 0.10
D)Fail to reject H₀ for all levels of significance.

Question 40

A Wilcoxon rank sum test for comparing two populations involves two independent samples of sizes 15 and 20.The un-standardized test statistic (that is the rank sum)is T = 225.The value of the standardized test statistic z is:

A)6)0
B)15
C)6)43
D)-1.5

Question 41

A chi-square goodness-of-fit-test is to be used to determine if a distribution is normally distributed.The data will be divided into "k" categories.Both the mean and standard deviation must be estimated.The degrees of freedom for this test would be:

A)k - 1
B)k - 2
C)k - 3
D)k - 4

Question 42

In a goodness-of-fit-test,suppose a sample showed that the observed frequency and expected frequency were equal for each cell i.Then,the null hypothesis is:

A)rejected at α = 0.05 but is not rejected at α = 0.025.
B)not rejected at any α level.
C)not rejected at α = 0.05 but is rejected at α = 0.025.
D)rejected at any level α.

Question 43

In the sign test applications,the normal approximation to the binomial distribution may be used whenever the number of nonzero differences exceeds:

A)5
B)10
C)20
D)15

Question 44

The decision rule in a chi-square goodness-of-fit-test is to reject the null hypothesis if the computed chi-square test statistic is:

A)greater than the table chi-square value.
B)less than the table chi-square value.
C)greater than zero.
D)greater than the number of categories.

Question 45

Under the null hypothesis that the population distribution is normal,the test statistic for the Jarque-Bera test for normality has a chi-square distribution with degrees of freedom equal to:

A)1
B)2
C)3
D)4

Question 46

A chi-square goodness-of-fit-test is to be used to determine if data fit a Poisson distribution.The data is divided into "k" categories.The mean number of occurrences is unknown and must be estimated.The degrees of freedom for this test would be:

A)k - 1
B)k - 2
C)k - 3
D)k - 4

Question 47

If a sample of 12 observations is taken to perform a matched or paired sign test and there are 2 ties in the data,then the p-value is based on a binomial distribution with:

A)n = 12,and P = 0.5
B)n = 10,and P = 0.5
C)n = 10,and P = 0.4
D)n = 12,and P = 0.4

Question 48

A researcher believes that a variable is Poisson distributed across six categories.To test this,a random sample is selected,and one parameter is estimated.Using α = 0.05,the critical chi-square value for this goodness-of-fit test is:

A)11.143
B)11.071
C)7.779
D)9.488

Question 49

In a goodness-of-fit-test,the null hypothesis states that the data has been obtained from a normally distributed population.The researcher estimated the population mean and population standard deviation from a sample of 400 observations.In addition,the researcher used 6 categories to test for normality.Using a 5% level of significance,the critical value for this test is:

A)7.815
B)5.991
C)11.071
D)9.488

Question 50

The Wilcoxon signed rank test statistic is approximately normally distributed whenever the number n of nonzero differences in the sample is larger than:

A)10
B)20
C)5
D)15

Question 51

A nonparametric method that is equivalent to the Wilcoxon rank sum test is the:

A)Wilcoxon signed rank test.
B)Sign test.
C)Spearman rank correlation test.
D)Mann-Whitney U test.

Question 52

A chi-square goodness-of-fit-test is to be performed to see if data fit the Poisson distribution.There are 5 categories,and the parameter λ must be estimated.How many degrees of freedom should be used?

A)5
B)4
C)3
D)2

Question 53

Which of the following tests employs matched-pairs sampling?

A)The Wilcoxon signed rank test
B)The Wilcoxon rank sum test
C)The Mann-Whitney test
D)The Durbin-Watson test

Question 54

Which of the following will never be a required condition of a nonparametric test?

A)Data used for the test are ordinal data.
B)Data used for the test are interval data.
C)The samples are drawn from normally distributed populations.
D)The populations being compared are identical in spread and shape.

Question 55

When the number n of nonzero differences in the sample is greater than 20,which of the following distributions provide a good approximation to the distribution of the Wilcoxon signed rank statistic?

A)The chi-square distribution
B)The normal distribution
C)The F distribution
D)The Student's t distribution

Question 56

Which statistical technique is appropriate when we wish to analyze the relationship between two qualitative variables with two or more categories?

A)The chi-square test of a multinomial experiment
B)The chi-square test of a contingency table
C)The t-test of the difference between two means
D)The z test of the difference between two proportions

Question 57

The sampling distribution for a goodness of fit test is the:

A)binomial distribution.
B)Student's t distribution.
C)chi-square distribution.
D)normal distribution.

Question 58

Consider the following data set: 12.2,12.3,12.3,12.5,12.6,12.7,12.8,12.8,12.8,12.9,13.1,13.2,and 13.5.The rank assigned to the three observations of value 12.8 is:

A)6
B)7
C)8
D)9

Question 59

In the sign test for paired differences,the test statistic S is the:

A)sum of the ranks of the data values.
B)number of ties in the data.
C)number of pairs with a positive difference.
D)number of pairs with nonzero differences.

Question 60

In goodness-of-fit-test,the expected frequencies are based on the:

A)null hypothesis.
B)alternative hypothesis.
C)normal distribution.
D)chi-square distribution.

Question 61

Nonparametric tests are often preferred to parametric tests since they do not rely on the normality assumption of the underlying population distribution.

Question 62

The Wilcoxon signed rank test provides a more accurate estimate of the p-value than the sign test for the same data.

Question 63

The simplest nonparametric test to carry out is the Wilcoxon rank sum test.

Question 64

We would typically use nonparametric tests only for ordinal data.

Question 65

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A sample of 10 observations produces the following summary values:
= 10815.472,
= 72.48 and S² = 28.044
What is the approximate value of kurtosis?

A)0.049
B)1.375
C)0.221
D)1.173

Question 66

Nonparametric tests are preferred to parametric tests since they are always more powerful.

Question 67

The test statistic for the Jarque-Bera test for normality does not depend on the:

A)measure of skewness.
B)measure of kurtosis.
C)sample size.
D)tied values in the data set.

Question 68

When testing for independence in a contingency table with r rows and c columns,the degrees of freedom for the test statistic would be:

A)r + c + 1
B)r + c -1
C)(r-1)(c-1)
D)rc - 1

Question 69

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A sample of 10 observations produces the following summary values:
= 10815.472,
= 72.48 and S² = 28.044
What is the approximate value of skewness?

A)0.049
B)0.221
C)1.375
D)1.173

Question 70

When using the chi-square goodness-of-fit-test,a statistician needs to make certain that none of the expected frequencies (or values)are less than:

A)the number of categories.
B)5
C)10
D)30

Question 71

For a large sample,the Wilcoxon rank sum test can be approximated by the Student's t distribution with (n - 1)degrees of freedom.

Question 72

A random sample of n observations,each of which could be classified into exactly one of k categories,is selected.Suppose that a null hypothesis specifies category probabilities that depend on the estimation of m unknown population parameters.How many degrees of freedom does a goodness-of-fit-test have when population parameters are estimated?

A)k - 1
B)m - 1
C)k - m - 1
D)k + m - 1

Question 73

A chi-square test of association in a contingency table with r rows and c columns has a chi-square distribution with rc-1 degrees of freedom.

Question 74

In order not to violate the requirements necessary to use the chi-square distribution,each expected frequency in a goodness-of-fit-test must be:

A)at most 5.
B)at least 5.
C)at least 10.
D)at most 10.

Question 75

The Wilcoxon rank sum test is likely to generate the same results as the Mann-Whitney U test.

Question 76

The sign test can be used to perform tests about the median for one population or to compare two population medians.

Question 77

The coefficients of skewness and kurtosis,under the null hypothesis that the population distribution is normal,are:

A)0 and 3 respectively.
B)3 and 0 respectively.
C)1 and 4 respectively.
D)4 and 1 respectively.

Question 78

To determine whether a single coin is fair,the coin was tossed 100 times,and the head was observed 60 times.The value of the test statistic is:

A)0.40
B)1.05
C)0.6
D)1.9

Question 79

A test that is conducted to determine whether or not to reject a hypothesized probability distribution is known as a:

A)test of independence.
B)contingency table test.
C)probability distribution test.
D)goodness-of-fit test.

Question 80

The figures used in calculating the test statistic X² =
are the observed and expected numbers in each of the k categories.However,it is correct,for example,to use instead the percentages of sample members in each category.