Deck 8: Data Analysis and Statistical Methods: Univariate and Bivariate Analyses

Question 1

The usual starting point in hypothesis testing is to specify the level of Type II error the researcher is willing to tolerate.

Answer 1

False
The level of Type I error is specified by the researcher.

Question 2

Normal distributions are bimodal.

Answer 2

False
Normal distributions are unimodal.

Question 3

When the sample size is small (< 25),the t and z distributions are very close to one another.

Answer 3

False
The distributions are close to each other when the sample size is large (> 30).

Question 4

In hypothesis testing,researchers never "accept" a null hypothesis,merely "fail to reject."

Question 5

Because hypotheses are always tested with data from a sample,there will always be some sampling error.

Question 6

The chi-square test can be used to test a hypothesized population distribution across nominal categories.

Question 7

Relative and absolute frequencies are appropriate measures of dispersion for nominal data.

Question 8

Both descriptive and inferential techniques must be chosen to match the scale level (nominal,ordinal,or interval)inherent in the variable(s)being analyzed.

Question 9

A statistic that is resistant to large changes when the data changes slightly is said to be bimodal.

Question 10

A Type II error has occurred if the null hypothesis is true and it is rejected.

Question 11

The median is robust,but the mean is not.

Question 12

The standard deviation is appropriate as a measure of dispersion for ordinal data.

Question 13

A "two-tailed test" is used to test the alternative hypothesis that a sample statistic is less than a particular value.

Question 14

In hypothesis testing,it is very difficult to make both $\alpha$ and $\beta$ small at the same time.

Question 15

Descriptive statistics are used to make inferences about a population.

Question 16

Sometimes variables may be bimodal,which means that two categories have similar,and relatively high,frequencies.

Question 17

For interval data,the chi-square test is the most appropriate inferential statistical test.

Question 18

The mode is defined as the middle value when data are arranged in order of magnitude.

Question 19

The z-test is an appropriate inferential statistical method for ordinal data if the sample size is large and the population standard deviation is not known.

Question 20

Three measures of dispersion are often used in marketing research: the mean,the median,and the mode.

Question 21

The F-test measures the proportion of variation in the dependent variable explained by the entire model,including all the independent variables taken together.

Question 22

The _______________ is an especially important and useful measure when data contain outliers.

A) mean
B) standard deviation
C) mode
D) median

Question 23

The median is not applicable for

A) nominal variables
B) ordinal variables
C) interval variables
D) a and c

Question 24

The _______________ is an appropriate measure of central tendency for interval data and is by far the most widely used measure in all of statistics.

A) mean
B) standard deviation
C) mode
D) median

Question 25

The alternative hypothesis should be stated as a parameter being

A) not equal to the value in H₀
B) equal to the value in H₀
C) greater than the value in H₀
D) less than the value in H₀
E) either a, c, or d

Question 26

Inferential statistics use probability theory to

A) make statements about the population
B) make statements about a sample
C) describe a sample
D) describe the overall distribution of samples

Question 27

A first step in almost all marketing research projects is to get a feel for the data by performing a

A) multivariate analysis on most of the available variables
B) bivariate analysis on the independent and dependent variable
C) linear regression on most of the available variables
D) univariate analysis on most of the available variables

Question 28

If the significance level for a hypothesis test is set at 0.03,the confidence level of the test would be

A) 0.03
B) 0.09
C) 0.97
D) determined by the researcher

Question 29

The goal of regression analysis is to predict a value for the independent variable based on knowledge of the dependent variable.

Question 30

In hypothesis testing,the Greek letter beta ( $\beta$ )refers to

A) the null hypothesis
B) the alternative hypothesis
C) Type I error
D) Type II error

Question 31

Type I error occurs when

A) H₀ is true and is rejected
B) H₀ is true and is not rejected
C) H₀ if false and is rejected
D) H₀ is false and is not rejected

Question 32

The _______________ is a measure of central tendency appropriate for nominal data.

A) chi-square test
B) variance
C) mode
D) median

Question 33

The appropriate measure of dispersion for nominal data is

A) the standard deviation
B) absolute frequencies
C) relative frequencies
D) both b and c

Question 34

A researcher will set the maximum tolerable degree of Type I error,which is referred to as the

A) confidence level of the test
B) significance level
C) power of the test
D) standard deviation

Question 35

In hypothesis testing,the null hypothesis is stated as a population parameter being

A) not equal to a particular value
B) equal to a particular value
C) being greater than a particular value
D) being less than a particular value
E) either a, c, or d

Question 36

The measures of central tendency include all of the following except

A) mean
B) standard deviation
C) mode
D) median

Question 37

When the total variation of a regression equation has been decomposed into that attributable to the regression,the remainder is attributable to error.

Question 38

The appropriate measure of dispersion for interval data is

A) the standard deviation
B) absolute frequencies
C) relative frequencies
D) both b and c

Question 39

If the coefficient of determination (r²)for a multiple regression is large,then the regression is highly significant.

Question 40

The linear correlation coefficient is scale-dependent,because the scale of the two variables will impact the correction coefficient.Changing one or both scales will change the coefficient.

Question 41

Given the problem,hypothesis,and test procedure stated in questions #20 through 23,a calculated test value of 1.78 is obtained.What conclusion is possible,assuming a 95 percent confidence level?

A) H₀ is not rejected.
B)H₀ is rejected.
C) $\pi$ in reality equals neither 0.25 nor 0.38.
D) No statement is possible; more information required.

Question 42

In using a univariate chi-square test of distributions for data that has 5 categories the degrees of freedom that would be used to determine the chi-square test statistic would be

A) 3
B) 4
C) 5
D) 6

Question 43

For questions #20 through 24 relate back to this situation:
A product manager is concerned with whether or not her product's share is equal to 25 percent of the market. A sample of 35 data points yields a sample proportion equal to 38 percent.

-What is the proper hypothesis specification,given the situation outlined above?

A) H₀: $\pi$ = 0.38; H₁: $\pi$$\neq$ 00.38
B) H₀: $\pi$ $\geq$ 0.38; H₁: $\pi$$\lt$ 0.38
C) H₀: $\pi$$\le$ 0.25; H₁: $\pi$$\gt$ 100.25
D) H₀: $\pi$ =0.25; H₁: $\pi$$\neq$ 0.25
E) More information is needed to determine the hypotheses.

Question 44

The z-test is appropriate for interval data when the sample

A) is of any size and the population standard deviation is known
B) is small and the population standard deviation is known
C) is of any size and the sample standard deviation is known
D) is large and the sample standard deviation is known

Question 45

The effect of units is eliminated by dividing the covariance by the standard deviation of the two variables to calculate a measure called the

A) scale independent relationship
B) linear correlation coefficient
C) coefficient of determination
D) least sum of squares

Question 46

The smaller a researcher sets the significance level,the

A) larger the probability of Type I error
B) larger the probability of Type II error
C) smaller the probability of Type II error
D) smaller the confidence level

Question 47

NOTE: For questions #20 through 24 relate back to this situation:
A product manager is concerned with whether or not her product's share is equal to 25 percent of the market. A sample of 35 data points yields a sample proportion equal to 38 percent.
What would be the numerator of the inferential statistical test for the hypothesis in question #20?

A) 0.13
B) -0.13
C) (0.13)²
D) 1-(0.13)²
E) none of the above

Question 48

NOTE: For questions #20 through 24 relate back to this situation:
A product manager is concerned with whether or not her product's share is equal to 25 percent of the market. A sample of 35 data points yields a sample proportion equal to 38 percent.
What inferential statistical test is appropriate for the hypothesis in question #20?

A) chi-square
B) F-test
C) t-test
D) z-test
E) none of the above

Question 49

Simple regression is appropriate for determining how

A) multiple dependent variables are related to one independent variable
B) multiple independent variables are related to one dependent variable
C) one independent variable is related to one dependent variable
D) one low-coefficient variable is related to one high-coefficient variable

Question 50

Once a sample statistic is obtained and compared to the value specified by the null hypothesis,the null hypothesis can be rejected if the difference

A) is greater than zero
B) is greater than that due to sampling error
C) between the standard deviations is above 1.96
D) is greater than what is stated in the alternative hypothesis

Question 51

The power of a hypothesis test is described as the probability of

A) rejecting a true null hypothesis
B) rejecting a false null hypothesis
C) not rejecting a true null hypothesis
D) not rejecting a false null hypothesis

Question 52

In general,the degrees of freedom (df )is the size of the sample (n)

A) plus the number of parameters estimated in the sample
B) minus the number of parameters estimated in the sample
C) minus (- X_i )²
D) divided by the number of parameters estimated in the sample

Question 53

The most important descriptive statistical procedure appropriate for use with two interval variables is the

A) z-test
B) t-test
C) simple linear regression
D) chi-square test

Question 54

Bivariate analysis would be needed to answer all of the following questions except:

A) Is our sample equally distributed among income categories?
B) What is the relationship between the heavy users of our brand and media viewing habits?
C) Are higher levels of sales associated with sales training attendance?
D) Do gas prices help predict sales of recreational boats?

Question 55

The effects of sample size can be corrected for by taking the SS_XY value for variables X and Y and _______________ to calculate the "covariance."

A) subtracting the mean of the variable
B) dividing it by the degrees of freedom of the sample
C) dividing it by the standard deviations of X and Y
D) using a chi-square test

Question 56

The _______________ is a procedure for comparing a hypothesized population distribution across nominal categories against an observed distribution.

A) t-test
B) z-test
C) chi-square test
D) linear regression

Question 57

In examining the relationship between two variables,if r = -1,then the relationship is

A) a perfect positive correlation
B) a perfect negative correlation
C) not a relationship at all
D) sorely in need of counseling

Question 58

The exact percentage of variation shared by two variables is calculated by squaring r,which is called the

A) scale-independent relationship
B) linear correlation coefficient
C) coefficient of determination
D) least sum of squares

Question 59

Given the following abbreviated table of critical values,

For the hypothesis in question #20,what is the appropriate critical value if one wants a 95 percent confidence level?

A) 1.64
B) 1.96
C) 2.24
D) 2.33
E) 2.47
F) none of the above

Question 60

The linear correlation coefficient measures the

A) linear relationship between two variables, X and Y
B) causal relationship between two variables, X and Y
C) degree of curvature (from elliptical to a straight line) between two variables, X and Y
D) relationship between two nominal variables, X and Y

Question 61

What is the power of the test and how does it relate to error?

Question 62

Identify and describe the types of error,their associated terminology and symbology,and how they are generally encountered in hypothesis testing.

Question 63

Define,and describe the relationship between,SS_XY,covariance,the linear correlation coefficient,the coefficient of determination,and r²-adjusted.

Question 64

What are a z-test and a t-test,and when should each be used?

Question 65

Outline the steps involved in hypothesis testing.

Question 66

Identify the three types of measures of central tendency.Discuss when each is appropriate to use.

Question 67

To use the chi-square test with the cross-tabulation of nominal data,expected cell sizes should be _______________ or greater.

A) 5
B) 10
C) 18
D) 30

Question 68

In a regression equation,the slope indicates the

A) increase in the dependent variable if the independent variable changes by one unit
B) increase in the independent variable if the dependent variable changes by one unit
C) point the regression line crosses the Y-axis
D) point the regression line crosses the X-axis

Question 69

Given the null hypothesis H₀ : $\mu$ = 10,what alternative hypothesis would require a two-tailed test?

Question 70

Describe the difference between descriptive and inferential statistics.

Question 71

If additional independent (X)variables are added into the regression equation,r² will always get larger.To correct for this situation,statisticians have developed the _______________,which is not so easily influenced by additional variables.

A) least sum-of-squares
B) r²-adjusted
C) standard error
D) coefficient of determination

Question 72

Based on the following array of data,calculate the mean,median,mode,and the absolute frequency of the value "10."
Data: 14,23,10,12,11,5,7,16,10

Question 73

If the relationship between two variables has a linear correlation coefficient (r)= 0.30,what is the coefficient of determination?

Question 74

The total variation,or sum-of-squares,of the dependent variable in a regression equation can be partitioned into

A) variation explained by the independent variable and variation explained by the dependent variable
B) variation explained by X and the variation explained by Y
C) variations explained by each of the independent variables
D) variation explained by regression and variation unexplained by regression

Question 75

To determine if there is a relationship between two nominal variables,researchers would use

A) simple regression
B) cross-tabulation and chi-square test on the two variables being independent
C) cross-tabulation and relative frequencies of independent variables
D) bivariate regression