Chapter 10 and 11 Probability and Statistics

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1

Which of the following is not a requirement for regression​ analysis?

A.Visual examination of the scatterplot shows that the points approximate a​ straight-line pattern.

B.Outliers can have a strong effect on the regression​ equation, so remove any outliers if they are known to be errors.

C.The sample of paired​ (x,y) data is a random sample of quantitative data.

D.The method for regression analysis line is not robust. It is seriously affected by a small departure from a normal distribution.

D.The method for regression analysis line is not robust. It is seriously affected by a small departure from a normal distribution.

2

A​ __________ exists between two variables when the values of one variable are somehow associated with the values of the other variable.

Correlation

3
card image

Regression of Diameter and Circumference

...

4

The​ _______ is a nonparametric test that uses ranks of sample data consisting of matched pairs used to test for an association between two variables.

Rank Correlation Test

5

Which of the following is not a requirement for regression​ analysis?

A.The sample of paired​ (x,y) data is a random sample of quantitative data.

B.The method for regression analysis line is not robust. It is seriously affected by a small departure from a normal distribution.This is the correct answer.

C.Outliers can have a strong effect on the regression​ equation, so remove any outliers if they are known to be errors.

D.Visual examination of the scatterplot shows that the points approximate a​ straight-line pattern.

B.The method for regression analysis line is not robust. It is seriously affected by a small departure from a normal distribution.This is the correct answer.

6

Which of the following is NOT a key component of the rank correlation​ test?

A.There is a requirement that any population has a normal distribution.This is the correct answer.

B.There is no requirement that the sample pairs of data have a bivariate normal distribution.

C.An alternative hypothesis for the rank correlation test is that there is a correlation between the two variables.

D.The paired data are a simple random sample.

A.There is a requirement that any population has a normal distribution.This is the correct answer.

7

Given a collection of paired sample​ data, the​ ____________________ y hat =b0+b1x algebraically describes the relationship between the two​ variables, x and y.

Regression equation

8

Which of the following is NOT true for the rank correlation​ test?

A.The method of rank correlation is more efficient than the method of linear correlation.This is the correct answer.

B.With rank​ correlation, we can analyze paired data that are ranks or can be converted to ranks.

C.Rank correlation can be used to detect some relationships that are not linear.

D.The nonparametric method of rank correlation can be used in a wider variety of circumstances than the parametric method of linear correlation.

A.The method of rank correlation is more efficient than the method of linear correlation.This is the correct answer.

9

Which of the following is not equivalent to the other​ three?

Explanatory variable

Predictor variable

Dependent variableThis is the correct answer

Independent variable

Dependent variableThis is the correct answer

10

Which of the following is NOT a requirement to conduct a​ goodness-of-fit test?

A.For each​ category, the observed frequency is at least 5.This is the correct answer.

B.The sample data consist of frequency counts for each of the different categories.

C.For each​ category, the expected frequency is at least 5.

D.The data have been randomly selected.

A.For each​ category, the observed frequency is at least 5.This is the correct answer.

11

Which of the following is NOT true of the​ goodness-of-fit test?

A.Expected frequencies need not be whole numbers.

B.If expected frequencies are​ equal, then we can determine them by Upper E equals StartFraction n Over k EndFractionE=nk​, where n is the total number of observations and k is the number of categories.

C.If expected frequencies are not all​ equal, then we can determine them by Eequals=np for each individual​ category, where n is the total number of observations and p is the probability for the category.

D.​Goodness-of-fit hypothesis tests may be​ left-tailed, right-tailed, or​ two-tailed.

D.​Goodness-of-fit hypothesis tests may be​ left-tailed, right-tailed, or​ two-tailed.

12

In a test of​ homogeneity, which of the following is NOT​ true?

A.If the chi squaredχ2 test statistic is​ large, the​ P-value will be small.

B.The null hypothesis is that the different populations have the same proportions of some characteristics.

C.Small values of the chi squaredχ2 test statistic would lead to a decision to reject the null hypothesis.This is the correct answer.

D.Samples are drawn from different populations and we wish to determine whether these populations have the same proportions of the characteristics being considered.

C.Small values of the chi squaredχ2 test statistic would lead to a decision to reject the null hypothesis.This is the correct answer.

13

A​ _____________ is used to test the hypothesis that an observed frequency distribution fits​ (or conforms​ to) some claimed distribution.

Goodness-of-fit Test

14

In a​ ____________ we test the claim that different populations have the same proportions of some characteristics.

Test of Homogeneity

15

Which of the following is NOT true of the χ2 test​ statistic?

A.If the observed and expected frequencies are not​ close, the chi squaredχ2 test statistic will be large and the​ P-value will be small.

B.A small chi squaredχ2 test statistic leads us to conclude that there is not a good fit with the assumed distribution.This is the correct answer.

C.The chi squaredχ2 test statistic is based on differences between the observed and expected values.

B.A small chi squaredχ2 test statistic leads us to conclude that there is not a good fit with the assumed distribution.This is the correct answer.

16

Which of the following is NOT a requirement of conducting a hypothesis test for independence between the row variable and column variable in a contingency​ table?

A.For every cell in the contingency​ table, the observed​ frequency, O, is at least 5.This is the correct answer.

B.For every cell in the contingency​ table, the expected​ frequency, E, is at least 5.

C.The sample data are randomly selected.

D.The sample data are represented as frequency counts in a​ two-way table.

A.For every cell in the contingency​ table, the observed​ frequency, O, is at least 5.This is the correct answer.

17

The method of​ _______ is used for tests of hypotheses that three or more population means are equal.

One-Way Analysis of Variance

18

Which of the following is NOT true of​ one-way analysis of variance experimental​ design?

A.Using a rigorously controlled design is one way to reduce the effect of extraneous factors.

B.Good results require that experiments be carefully designed and executed.

C.In any​ design, if the conclusion is that the differences among the means are​ significant, the differences are explained by the factor used.This is the correct answer

.D.A completely randomized experimental design is one way to reduce the effect of extraneous factors.

C.In any​ design, if the conclusion is that the differences among the means are​ significant, the differences are explained by the factor used.This is the correct answer

19

A​ ____________ is a table in which frequencies correspond to two variables.

Contingency Table

20

Which of the following is NOT a requirement for using​ one-way analysis of variance for testing equality of three of more population​ means?

A.The samples are matched or paired in some way.This is the correct answer.

B.The samples are simple random samples of quantitative data.

C.The populations have distributions that are approximately normal.

D.The different samples are from populations that are categorized in only one way.

A.The samples are matched or paired in some way.This is the correct answer.

21

A​ _______ is a characteristic used in ANOVA that allows us to distinguish different populations from one another.

Treatment

22

Which of the following is NOT true of the F test​ statistic?

A.Fequals=StartFraction MS left parenthesis treatment right parenthesis Over MS left parenthesis error right parenthesis EndFractionMS(treatment)MS(error)​, when testing with unequal sample sizes

B.The F test statistic is never negative.

C.If the F test statistic is​ large, then the​ P-value will be large. This is the correct answer.

D.Fequals=StartFraction left parenthesis variance between samples right parenthesis Over left parenthesis variance with samples right parenthesis EndFraction

C.If the F test statistic is​ large, then the​ P-value will be large. This is the correct answer.

23

Which of the following is NOT true for conducting a hypothesis test for independence between the row variable and column variable in a contingency​ table?

A.The number of degrees of freedom is ​(rminus−​1)(cminus−​1), where r is the number of rows and c is the number of columns.

B.The null hypothesis is that the row and column variables are independent of each other.

C.Small values of the chi squaredχ2 test statistic reflect significant differences between observed and expected frequencies.This is the correct answer.

D.Tests of independence with a contingency table are always​ right-tailed.

C.Small values of the chi squaredχ2 test statistic reflect significant differences between observed and expected frequencies.This is the correct answer.

24

Which of the following is NOT a procedure​ (either formal or​ informal) to use to identify the specific means that are different when the conclusion of a​ one-way ANOVA is that at least one of the population means is​ different?

A.Utilize multiple comparison tests that make adjustments to overcome the problem of increasing the probability of a Type I error.

B.Use a range test to identify subsets of means that are not significantly different from each other.

C.Utilize​ Bayes' Theorem to differentiate at least one mean from the others.This is the correct answer.

D.Construct boxplots of the data sets to see if one or more is significantly different from the others.

C.Utilize​ Bayes' Theorem to differentiate at least one mean from the others.This is the correct answer.