Deck 19: Data Analysis: Analyzing Individual Variables and Basics of Hypothesis Testing

Question 1

A chart where the values of the variable are placed along the abscissa,the absolute frequency or relative frequency of occurrence of the values are indicated along the ordinate,and the midpoints of the bars are connected is a

A)matrix.
B)cumulative distribution function.
C)histogram.
D)frequency polygon.
E)midpoint chart.

Answer 1

D

Question 2

Which of the following would NOT be an example of a situation involving univariate analysis?

A)A publisher of a magazine is interested in determining what proportion of the magazine's readers is male.
B)A restaurant would like to know the average income of its typical diner.
C)A car dealership is particularly interested in whether or not people who own vans are more or less likely to finance auto purchases compared with people who don't own vans.
D)A service provider needs to know her customer's average level of satisfaction with the services provided.
E)All of the above are examples for which univariate analysis could be performed.

Answer 2

C

Question 3

The one-way tabulation does NOT serve as a basic input for which of the following?

A)Histogram
B)Frequency polygon
C)Empirical cumulative distribution function
D)Calculating summary statistics
E)The development of a codebook

Answer 3

E

Question 4

A bar chart where the values of a variable are placed along the X-axis and the absolute or relative frequency along the Y-axis is called a ____ and can be developed from the ____.

A)bar graph,cumulative data
B)frequency polygon,one-way frequency tabulation
C)cumulative distribution graph,cumulative data
D)histogram,uncoded data
E)histogram,one-way frequency tabulation

Question 5

One method of visualizing the estimated distribution of the characteristic in question is to construct a

A)frequency polygon.
B)pie chart.
C)histogram.
D)Both a and c.
E)None of the above.

Question 6

Which types of measurement are used to group respondents or objects into groups or categories and are thus referred to as categorical measures?

A)Nominal and interval
B)Ordinal and ratio
C)Ratio and interval
D)Nominal and ordinal
E)Ordinal and interval

Question 7

Some of the commonly used measures of location such as the median or quartiles can be read directly from a

A)matrix.
B)frequency polygon.
C)histogram.
D)cumulative distribution function.
E)contingency table.

Question 8

An observation that is very different in magnitude from the rest of the observations for a particular variable is a(n)

A)error.
B)blunder.
C)histogram.
D)outlier.
E)deviant.

Question 9

Data analysis hinges on which of the following considerations about the variable(s)to be analyzed?

A)Will the variable be analyzed in isolation or in relationship to one or more other variables?
B)What type of analysis is required by the project sponsor?
C)What level of measurement was used to measure the variable(s)?
D)Both a and c.
E)All of the above are considerations about the variable(s)to be analyzed.

Question 10

The one-way tabulation is NOT used to

A)locate blunders.
B)locate outliers.
C)determine the empirical distribution of the variable.
D)communicate the results of the study.
E)determine the relationship between two variables.

Question 11

Exhibit 19.2 Refer to Exhibit 19.2.What is the sample standard deviation?

A)0.4318
B)0.3246
C)0.6571
D)1.0239
E)Can't be determined from the table.

Question 12

Exhibit 19.1 Refer to Exhibit 19.1.The figure above is an example of a

A)cumulative distribution function.
B)frequency polygon.
C)histogram.
D)one-way tabulation of annual income per person.
E)midpoint chart.

Question 13

Which of the following is TRUE?

A)A frequency polygon is developed by connecting the points of change in a cumulative distribution function.
B)The frequency polygon is obtained from the histogram by connecting the midpoints of the bars with straight lines.
C)The empirical cumulative distribution function is obtained from the histogram by connecting the midpoints of the bars of the histogram with straight lines.
D)The empirical cumulative distribution function can only be generated from the cross tabulation.
E)Histograms are obtained from frequency polygons.

Question 14

Exhibit 19.2 Refer to Exhibit 19.2.What is the average number of televisions per household?

A)2.00
B)1.85
C)1.52
D)2.25
E)2.74

Question 15

Exhibit 19.1 Refer to Exhibit 19.1.$50,000 represents the ____ in the figure above.

A)median.
B)sixtieth percentile.
C)third quartile.
D)seventieth percentile.
E)None of the above.

Question 16

Exhibit 19.2 Refer to Exhibit 19.2.What is the modal number of televisions owned by the households in the sample?

A)2
B)More than 3
C)1
D)3
E)Can't be determined from the table.

Question 17

Exhibit 19.1 Refer to Exhibit 19.1.The median income in the above figure is

A)$10,000.
B)$20,000.
C)$30,000.
D)$50,000.
E)$100,000.

Question 18

Histograms are used to

A)investigate the relation between two variables.
B)construct cumulative distribution functions.
C)construct cross tabulation tables.
D)determine the distribution of nonresponse errors.
E)determine the empirical distribution of a variable.

Question 19

The one-way tabulation can be used to

A)locate blunders.
B)determine the empirical distribution of the variable in question.
C)determine the relationship between two variables.
D)Both a and b.
E)test hypotheses.

Question 20

Calculations for a one-way tabulation revealed that the percentage of men owning Dalmatians was 9.93472.Which of the following is the best way to display this finding in the tabulation?

A)(9.93472%)
B)9.93%
C)(10%)
D)(9%)
E)(9.9%)

Question 21

Exhibit 19.5 Refer to Exhibit 19.5.The estimated value of the standard error of the mean ( )is

A)0.6.
B)0.9.
C)1.6.
D)2.6.
E)3.0.

Question 22

Exhibit 19.6 120 field mice are weighed.The average weight of a mouse is 225 grams and the sample standard deviation is 15.1 grams.
Refer to Exhibit 19.6.What is the value of the test statistic for the hypothesis that the actual mean weight of the mouse population is greater than 235 grams?

A)-0.578
B)-2.79
C)-0.633
D)-6.33
E)-7.25

Question 23

A researcher is interested in analyzing a set of nominal data to determine if the observed pattern of frequencies corresponds to the expected pattern.The appropriate statistical technique is

A)chi-square goodness-of-fit.
B)regression analysis.
C)z-test for comparing sample proportion against a standard.
D)z-test for comparing sample mean against a standard.
E)frequency analysis.

Question 24

A researcher had calculated the sample chi-square test statistic to be equal to c² = 7.71.For an alpha level of 0.10 and 4 degrees of freedom,the critical value of the chi-square statistic is 7.78.The appropriate conclusion is that the

A)sample result is likely to be attributed to chance alone.
B)null hypothesis should not be rejected.
C)null hypothesis should be rejected.
D)Both a and b.
E)alternative hypothesis is true.

Question 25

An analyst is interested in testing the hypothesis Ho: m £ 15000.The data consist of 20 observations of an intervally scaled variable which is normally distributed,but with unknown variance.The correct statistical procedure is

A)z-test.
B)t-test.
C)regression analysis.
D)frequency analysis.
E)chi-square goodness-of-fit test.

Question 26

Exhibit 19.6 120 field mice are weighed.The average weight of a mouse is 225 grams and the sample standard deviation is 15.1 grams.
Refer to Exhibit 19.6.What is the estimated standard error of the mean?

A)0.173 grams
B)1.15 grams
C)1.38 grams
D)15.8 grams
E)17.3 grams

Question 27

Which of the following statements is FALSE? The t-test to test a hypothesis about a single population mean

A)assumes the variable is normally distributed.
B)applies when the variance of the variable is known.
C)applies when the sample size is small;e.g. ,less than 30.
D)applies when the distribution of the variable in the population is assumed to be at least symmetrical.
E)All of the above are true.

Question 28

A researcher calculates a chi-square test statistic of 8.56.At a = .05 and n = 3,the critical value of the chi-square statistic is 7.81.What is the appropriate statistical conclusion?

A)Reject the null hypothesis.
B)Can't determine;not enough information given.
C)Fail to reject the null hypothesis.
D)Reject the alternative hypothesis.
E)Conclude that the null hypothesis is true.

Question 29

To calculate sampling error for a proportion,which of the following pieces of information is NOT needed?

A)The z-score representing the desired degree of confidence.
B)The number of valid cases overall for the proportion.
C)The sample standard deviation.
D)The relevant proportion obtained from the sample.
E)All of the above are relevant and necessary pieces of information for the calculation of sampling error for a proportion.

Question 30

Exhibit 19.5 Refer to Exhibit 19.5.The estimated value of the test statistic is

A)4.0
B)5.2
C)6.7
D)7.2
E)9.0

Question 31

Exhibit 19.5 Refer to Exhibit 19.5.The degrees of freedom would equal

A)14.
B)24.
C)219.
D)199.
E)Cannot tell from the given information.

Question 32

Exhibit 19.6 120 field mice are weighed.The average weight of a mouse is 225 grams and the sample standard deviation is 15.1 grams.
Refer to Exhibit 19.6.The conclusion is

A)The mean weight of a field mouse is greater than 235 grams.
B)The mean weight of a field mouse is less than 235 grams.
C)Estimate a point mean of 235 grams.
D)The mean weight of a field mouse is less than 225 grams.
E)None of the above are correct.

Question 33

Exhibit 19.3 Use the information below to answer the questions.
A major car manufacturer was interested in whether its midsize car was selling consistently in two markets with respect to the annual income of the car purchasers.500 new car buyers in Chicago and Miami were surveyed.In Chicago the following pattern was observed:
Among those surveyed in Miami,20 earned under $20,000;70 earned between $20,000 and $30,000;265 earned between $30,000 and $40,000;125 earned between $40,000 and $50,000;and 20 earned more than $50,000.
Refer to Exhibit 19.3.The chi-square test was used to check whether Miami sales among income groups were consistent with Chicago's.The appropriate degrees of freedom for the chi-square test would be

A)4
B)5
C)500
D)499
E)None of the above.

Question 34

Which of the following statements concerning confidence intervals is FALSE?

A)A confidence interval can be inferred when a probabilistic sample is drawn.
B)A confidence interval is produced by calculating the degree of nonsampling error for the particular statistic.
C)Precision can be increased by increasing sample size or decreasing the confidence level.
D)A narrower confidence interval can be obtained by increasing the sample size.
E)A narrower confidence interval can be obtained by decreasing the degree of confidence desired.

Question 35

Which of the following is FALSE about the use of percentages when reporting results?

A)Unless decimals have a special purpose,they should be omitted.
B)Percentages should be rounded to whole numbers.
C)Decimals may convey greater accuracy than the figures can support.
D)It is unnecessary and redundant to include percentages along with the raw count for frequency analyses.
E)All of the above are true concerning the use of percentages when reporting results.

Question 36

Exhibit 19.5 Refer to Exhibit 19.5.The appropriate test statistic for this problem would be a

A)z-test.
B)t-test.
C)Chi-square goodness-of-fit test.
D)variance.
E)Any of the above tests would be appropriate.

Question 37

The chi-square test is an approximate test.The approximation is relatively good if the

A)expected number of cases in each category is 10 or more.
B)expected number of cases in each category is 5 or more.
C)expected number of cases in each category is 3 or more.
D)actual number of cases in each category is 10 or more.
E)actual number of cases in each category is 5 or more.

Question 38

Exhibit 19.6 120 field mice are weighed.The average weight of a mouse is 225 grams and the sample standard deviation is 15.1 grams.
Refer to Exhibit 19.6.What is the 95% confidence interval for the average weight of a field mouse? (z = 1.96)

A)222 to 228 grams
B)217 to 223 grams
C)221 to 229 grams
D)240 to 245 grams
E)None of the above are correct.

Question 39

Which statement(s)pertaining to the chi-square distribution is FALSE?

A)The chi-square distribution is completely determined by its degrees of freedom.
B)The variable of interest is broken into k mutually exclusive categories.
C)The expected number falling into a category is generated from the null hypothesis.
D)Chi-square degrees of freedom is given by k - 2.
E)The chi-square is appropriate for independent trials.

Question 40

Exhibit 19.3 Use the information below to answer the questions.
A major car manufacturer was interested in whether its midsize car was selling consistently in two markets with respect to the annual income of the car purchasers.500 new car buyers in Chicago and Miami were surveyed.In Chicago the following pattern was observed:
Among those surveyed in Miami,20 earned under $20,000;70 earned between $20,000 and $30,000;265 earned between $30,000 and $40,000;125 earned between $40,000 and $50,000;and 20 earned more than $50,000.
Refer to Exhibit 19.3.Using the data provided,the calculated value of c² =

A)0.883
B)36.30
C)11.95
D)-0.542
E)Not enough information is provided to calculate the value.

Question 41

Which of the following is TRUE about hypothesis testing?

A)The typical goal is to reject the alternative hypothesis in favor of the null hypothesis.
B)A hypothesis may be rejected but can never be accepted completely.
C)Marketing research studies attempt to prove results.
D)The null hypothesis is assumed to be false for the purpose of the test.
E)All of the above are true about hypothesis testing.

Question 42

The one-tailed test is commonly used in marketing research because

A)there is typically some hypothesized or preferred direction to the outcome.
B)it is more powerful statistically than the two-tailed alternative.
C)it is easier to calculate than the two-tailed alternative.
D)Both a and b.
E)a,b,and c.

Question 43

When a sample mean is compared against a standard for a large sample,which statistic is calculated?

A)t
B)p
C)c²
D)s
E)z

Question 44

For which of the following types of measures does the mean NOT provide a meaningful value?

A)Ratio
B)Equal-interval scales
C)Interval
D)Ordinal
E)Continuous measures

Question 45

A research study that tests the hypothesis,"The population mean household income in the new market area is greater than $29,000," will involve a

A)test of two means.
B)test for a single mean.
C)test for a single proportion.
D)test of two proportions.
E)test of a single variance.

Question 46

A researcher determines a sample of size (n)100 is necessary to estimate a population mean with 95% confidence (z = 2).The calculation of sample size required that he estimate the population standard deviation since it was unknown,and he estimated it as 150.The 100 observations produced a sample mean and a sample standard deviation The resulting confidence interval is

A)970 < m < 1030.
B)996 < m < 1004.
C)997 < m < 1003.
D)960 < m < 1040.
E)There are two possible confidence intervals.

Question 47

Which of the following statements concerning the sample standard deviation is FALSE?

A)Sample standard deviation is a measure of the variation in responses.
B)Analysts reporting descriptive statistics for continuous measures should always report standard deviations along with mean values.
C)Standard deviation is meaningful and appropriate only for interval- and nominal-level measures.
D)An analyst must be aware of the concerns of spurious precision when reporting standard deviations.
E)Outliers can have a marked effect the calculation of a standard deviation.

Question 48

If the standard deviation of household income for a sample of 625 households is $8,000,what is the standard error of the mean?

A)$320
B)$625
C)$8,000
D)$80
E)$25

Question 49

Suppose that a random sample of 550 new car owners found that 38 percent of them were aware of a particular brand of tires that your company sells.If you are willing to accept less than a 5 percent chance of error that the true awareness rate of your company's brand of tire across all new car owners is less than 0.45,which statistical technique should you use from this data?

A)Test for a single proportion
B)Test of two means when samples are independent.
C)Test for a single mean.
D)Test of two means when samples are dependent.
E)ANOVA

Question 50

Which of the following would be an appropriate interpretation of a p-value?

A)A p-value of p < 0.0001 is 'highly significant' and therefore much more valid than a p value of 0.05.
B)When a null hypothesis is rejected at some predetermined p level,sampling error is an unlikely explanation of the results,given that the null hypothesis is true.
C)When a p-value shows significance,managerial and practical significance can be assumed.
D)The probability that the research hypothesis is true is equal to 1 minus the p-value.
E)A p-value represents the probability that the results occurred because of sampling error.

Question 51

Type I error

A)occurs when a true null hypothesis is rejected.
B)is usually referred to as significance level.
C)is symbolized by alpha (?).
D)a,b,and c.
E)None of the above are correct.

Question 52

A sample mean is compared against a standard for a large sample.Now,assume the sample mean was found to equal 40.What is the appropriate confidence interval? (Note: Round to the nearest whole number. )

A)23 < m < 57
B)Can't be determined from the information given.
C)14 < m < 66
D)38 < m < 42
E)20 < m < 60

Question 53

When using a z-test for comparing a sample mean against a standard,one must consider all of the following EXCEPT whether the

A)variance of the variable in the population is known or unknown.
B)distribution of the variable in the population is normal (or at least symmetrical)or asymmetrical.
C)mean falls within an acceptable confidence interval.
D)sample size is small or large.
E)All of the above must be considered.

Question 54

Which of the following is true regarding the standard deviation?

A)It indicates the degree of variation in the values in such a way as to be translatable into a normal curve.
B)One standard deviation above and below the midpoint in a normal distribution includes approximately 68% of the area underneath the curve.
C)+ or - 1.96 standard deviations above and below the midpoint in a normal distribution includes 95% of the area underneath the curve.
D)The standard deviation can be approximated by dividing the range of the data by 6.
E)All of the above are correct.

Question 55

Because ____ and ____ measures are similar when it comes to analysis,many researchers refer to both types as continuous measures.

A)interval,ratio
B)nominal,interval
C)ordinal,ratio
D)nominal,ordinal
E)ratio,nominal

Question 56

In the following data set,what is the median? 12,0,0,1,1,1,6,10,11.

A)4.66
B)1
C)42
D)6
E)0

Question 57

Which type of statistical analysis would we use to determine if female college graduates' starting salary was different from their male counterpart (assuming data is collected using the following question on the survey "What is your starting salary ____?"

A)Test of two means.
B)Test for a single mean.
C)Test for a single proportion.
D)Test of two proportions.
E)Test of a single variance

Question 58

Which of the following statements if FALSE concerning the conversion of continuous measures to categorical measures?

A)When converting,there is no loss of information about a variable.
B)Because higher levels of measurement have all the properties of measures lower in the hierarchy,conversion is perfectly acceptable.
C)In many cases,conversion is advisable for aiding in interpretation of research study results.
D)Analyses should be performed using the highest level of measurement possible for a particular variable.
E)A simple solution would be to provide both types of results.

Question 59

Descriptive statistics include all of the following measures EXCEPT

A)median.
B)confidence intervals.
C)skewness.
D)variance.
E)range.

Question 60

The FactFinder Research firm conducted a survey for a national food manufacturer and one of the issues addressed by the research was to determine how many pounds of fish were annually consumed per capita.In the survey they found one person who consumed only one pound of fish per year while 10 people reported 200 pounds per year.The range was

A)200.
B)1 to 2,000.
C)201.
D)199.
E)None of the above.

Question 61

Kit Kat candy bar executives make the following statement: "Our most likely estimate of Kit Kat's ad recall rate is 65%.In addition,we are 95% confident that Kit Kat's ad recall rate in the population falls between 62% and 68%." This illustrates an example of

A)basic descriptive statistics.
B)using statistical inference to estimate a population parameter based upon sample statistics.
C)using statistical inference to estimate a statistic based upon a population parameter.
D)hypothesis testing.
E)Both a and b.

Question 62

A histogram is a form of bar chart that is based on information from a frequency count.

Question 63

The acceptable level of Type 1 error is usually referred to as the significance level.

Question 64

A(n)____________________ interval is a projection of the range within which a population parameter will lie at a given level of confidence based on a statistic obtained from an appropriately drawn sample.

Question 65

You can "prove" that the alternative hypothesis is true if the null hypothesis is rejected.

Question 66

The more confidence we want to have in the interval estimate,the larger the sample size should be.

Question 67

The logic of hypothesis testing is that if we assume that the hypothesized value is the population parameter,then,at the 95% level of confidence,if we took 100 separate samples,the z-value for 95 of those samples would fall between + or - 1.96.

Question 68

The hypothesis that a proposed result is not true for the population is called the ____________________ hypothesis.

Question 69

To test directional hypotheses,you would use a two-tailed test.

Question 70

An outlier is an observation so different from the rest of the observations that the analyst chooses to treat it as a special case.

Question 71

Discuss the most commonly used descriptive statistics.

Question 72

A statistical test to determine whether some observed pattern of frequencies corresponds to an expected pattern is called a chi-square goodness-of-fit test.

Question 73

A sampling procedure is statistically more efficient than another procedure if,for a given sample size,it results in a larger sampling error.

Question 74

The use of the t-statistic in a hypothesis test with two means requires the assumption that it involves two independent samples.

Question 75

The arithmetic mean value across all responses for a variable is called the ____________________ mean.

Question 76

The ____________________ is a statistical test to determine whether some observed pattern of frequencies corresponds to and expected pattern.

Question 77

An observation so different in magnitude from the rest of the observations that the analyst chooses to treat it as a special case is called a(n)____________________.

Question 78

In using percentages for reporting results it is reasonable to report percentages to two decimal places.

Question 79

Both nominal and ordinal measures are easily used to group respondents or objects into groups or categories.