Deck 15: Categorical Versus Categorical: Tests

Question 1

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

Answer 1

True

Question 2

A chi-square goodness-of-fit test to determine if the observed frequencies in seven categories are uniformly distributed has six degrees of freedom.

Answer 2

True

Question 3

In a chi-square test of independence the contingency table has 4 rows and 3 columns. The number of degrees of freedom for this test is 6.

Answer 3

True

Question 4

The number of degrees of freedom in a chi-square goodness-of-fit test is the number of categories minus the number of parameters estimated minus one.

Question 5

A chi-square goodness-of-fit test to determine if the observed frequencies in ten categories are Poisson distributed has nine degrees of freedom.
Answer False

Question 6

A chi-square goodness-of-fit test is being used to test the goodness-of-fit of a uniform distribution for a dataset with "k" categories. This test has (k - 3) degrees of freedom.

Question 7

The null hypothesis in a chi-square goodness-of-fit test is that the observed distribution is the same as the expected distribution.

Question 8

A goodness-of-fit test is to be performed to see if Web Surfers prefer any of four websites (A, B, C and D) more than the other three. A sample of 60 consumers is used. What is the expected frequency for website A?

A) 1/4
B) 20
C) 15
D) 10
E) 30

Question 9

A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using $\alpha$ =.01, the degrees of freedom for this test are ___.

A) 5
B) 4
C) 3
D) 2
E) 1

Question 10

In a chi-square goodness-of-fit test, actual frequencies are also called calculated frequencies.

Question 11

A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using $\alpha$ =.01, the critical value of chi-square is ___.

A) 7.78
B) 15.09
C) 9.24
D) 13.28
E) 15.48

Question 12

The number of degrees of freedom in a chi-square goodness-of-fit test is the number of categories minus the number of parameters estimated.

Question 13

In a chi-square goodness-of-fit test, theoretical frequencies are also called expected frequencies.

Question 14

In a chi-square test of independence the contingency table has 4 rows and 3 columns. The number of degrees of freedom for this test is 7.

Question 15

A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using $\alpha$ =.01, the observed value of chi-square is ___.

A) 12.09
B) 9.82
C) 13.28
D) 17.81
E) 2.09

Question 16

The null hypothesis for a chi-square test of independence is that the two variables are not related.

Question 17

When using the chi-square goodness-of-fit test, the type of distribution (uniform, Poisson, normal) being used does not influence the hypothesis test.

Question 18

A researcher is interested in using a chi-square test of independence to determine if age is independent of minutes spent reading. Age is divided into four categories while minutes spent reading is classified as high, medium, low. The number of degrees of freedom for this test is 12.

Question 19

A goodness-of-fit test is to be performed to see if consumers prefer any of three package designs (A, B, and C) more than the other two. A sample of 60 consumers is used. What is the expected frequency for category A?

A) 1/3
B) 20
C) 60
D) 10
E) 30

Question 20

The decision rule in a chi-square goodness-of-fit test is to reject the null hypothesis if the computed chi-square is greater than the table chi-square.

Question 21

A suburban realtor is studying commuter time in the Calgary metropolitan area. She has been told the average weekday travel time from a southern suburb at 8:00 a.m. is 45 minutes. For five months she counts the number of days that it takes her more than 45 minutes to arrive in downtown when she leaves her house at 8:00 a.m. She expects the data are uniformly distributed across the five months. Her sample of observed data yields the following frequencies: 9 days, 15 days, 8 days, 11 days, 12 days. Using $\alpha$ =.01, the critical chi-square value is ___.

A) 13.277
B) 15.086
C) 7.779
D) 11.070
E) 2.727

Question 22

A suburban realtor is studying commuter time in the Calgary metropolitan area. She has been told the average weekday travel time from a southern suburb at 8:00 a.m. is 45 minutes. For five months she counts the number of days that it takes her more than 45 minutes to arrive in downtown when she leaves her house at 8:00 a.m. She expects the data are uniformly distributed across the five months. Her sample of observed data yields the following frequencies: 9 days, 15 days, 8 days, 11 days, 12 days. Using $\alpha$ =.01, the appropriate decision is ___.

A) do not reject the null hypothesis that the observed distribution is uniform
B) do not reject the null hypothesis that the observed distribution is not uniform
C) reject the null hypothesis that the observed distribution is uniform
D) reject the null hypothesis that the observed distribution is not uniform
E) do nothing

Question 23

A researcher believes that arrivals at a walk-in hair salon are Poisson distributed. The following data represent a distribution of frequency of arrivals in a one hour time period: Using $\alpha$ = 0.10, the observed chi-square value for this goodness-of-fit test is ___.

A) 2.28
B) 14.56
C) 17.43
D) 1.68
E) 2.67

Question 24

A chi-square goodness-of-fit test is to be performed to see if data fit the Poisson distribution. There are 6 categories, and λ must be estimated. How many degrees of freedom should be used?

A) 6
B) 5
C) 4
D) 3
E) 2

Question 25

A suburban realtor is studying commuter time in the Calgary metropolitan area. She has been told the average weekday travel time from a southern suburb at 8:00 a.m. is 45 minutes. For five months she counts the number of days that it takes her more than 45 minutes to arrive in downtown when she leaves her house at 8:00 a.m. She expects that data are uniformly distributed across the five months. Her sample of observed data yields the following frequencies: 9 days, 15 days, 8 days, 11 days, 12 days. Using $\alpha$ =.01, the observed chi-square value is ___.

A) 1.18
B) 9.10
C) 21.75
D) 4.51
E) 2.73

Question 26

A researcher believes that a variable is Poisson distributed across six categories. To test this, the following random sample of observations is collected: Using $\alpha$ = 0.10, the value of the observed chi-square for the data is ___.

A) 19.37
B) 2.29
C) 1.74
D) 3.28
E) 4.48

Question 27

A market researcher is studying the use of coupons by consumers of varying ages. She classifies consumers into four age categories and counts the number of grocery store customers who use at least one coupon during check out. It is expected that data are uniformly distributed across the four age categories. The observed data results in frequencies of 22, 35, 32, and 21. Using $\alpha$ =.05, the observed chi-square value is ___.

A) 5.418
B) 9.10
C) 20.27
D) 4.51
E) 7.86

Question 28

Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution. He collected a random sample and constructed the following frequency distribution to test his hypothesis: The number of degrees of freedom for this goodness-of-fit test is ___.

A) 5
B) 4
C) 3
D) 2
E) 1

Question 29

A researcher believes that a variable is Poisson distributed across six categories. To test this, the following random sample of observations is collected: Using $\alpha$ = 0.10, the critical value of chi-square for the data is ___.

A) 9.236
B) 1.064
C) 7.779
D) 13.277
E) 12.89

Question 30

A chi-square goodness-of-fit test is to be performed to see if data fit the Poisson distribution. There are 8 categories, and λ must be estimated. Alpha is chosen to be 0.10. The critical (table) value of chi-square is ___.

A) 10.645
B) 12.017
C) 3.828
D) 16.812
E) 17.345

Question 31

Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution. He collected a random sample and constructed the following frequency distribution to test his hypothesis: Using $\alpha$ = 0.05, the appropriate decision for this goodness-of-fit test is ___.

A) reject the null hypothesis that the observed distribution is Poisson
B) reject the null hypothesis that the observed distribution is not Poisson
C) do not reject the null hypothesis that the observed distribution is not Poisson
D) do not reject the null hypothesis that the observed distribution is Poisson
E) do nothing

Question 32

A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using $\alpha$ =.01, the appropriate decision is ___.

A) reject the null hypothesis that the observed distribution is uniform
B) reject the null hypothesis that the observed distribution is not uniform
C) do not reject the null hypothesis that the observed distribution is uniform
D) do not reject the null hypothesis that the observed distribution is not uniform
E) do nothing

Question 33

Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution. He collected a random sample and constructed the following frequency distribution to test his hypothesis: Using $\alpha$ = 0.05, the critical value of chi-square for this goodness-of-fit test is ___.

A) 9.49
B) 7.81
C) 7.78
D) 11.07
E) 12.77

Question 34

A researcher believes that arrivals at a walk-in hair salon are Poisson distributed. The following data represent a distribution of frequency of arrivals in a one hour time period: Using $\alpha$ = 0.10, the critical chi-square value for this goodness-of-fit test is ___.

A) 1.064
B) 13.277
C) 9.236
D) 8.799
E) 7.779

Question 35

A market researcher is studying the use of coupons by consumers of varying ages. She classifies consumers into four age categories and counts the number of grocery store customers who use at least one coupon during check out. It is expected that data are uniformly distributed across the four age categories. The observed data results in frequencies of 22, 35, 32, and 21. Using $\alpha$ =.05, the appropriate decision is ___.

A) do not reject the null hypothesis that the observed distribution is uniform
B) do not reject the null hypothesis that the observed distribution is not uniform
C) reject the null hypothesis that the observed distribution is uniform
D) reject the null hypothesis that the observed distribution is not uniform
E) do nothing

Question 36

A market researcher is studying the use of coupons by consumers of varying ages. She classifies consumers into four age categories and counts the number of grocery store customers who use at least one coupon during check out. It is expected that data are uniformly distributed across the four age categories. The observed data results in frequencies of 22, 35, 32, and 21. Using $\alpha$ =.10, the appropriate decision is ___.

A) do not reject the null hypothesis that the observed distribution is uniform
B) do not reject the null hypothesis that the observed distribution is not uniform
C) reject the null hypothesis that the observed distribution is uniform
D) reject the null hypothesis that the observed distribution is not uniform
E) do nothing

Question 37

A suburban realtor is studying commuter time in the Calgary metropolitan area. She has been told the average weekday travel time from a southern suburb at 8:00 a.m. is 45 minutes. For five months she counts the number of days that it takes her more than 45 minutes to arrive in downtown when she leaves her house at 8:00 a.m. She expects the data are uniformly distributed across the five months. Her sample of observed data yields the following frequencies: 9 days, 15 days, 8 days, 11 days, 12 days. Using $\alpha$ =.10, the appropriate decision is ___.

A) do not reject the null hypothesis that the observed distribution is uniform
B) do not reject the null hypothesis that the observed distribution is not uniform
C) reject the null hypothesis that the observed distribution is uniform
D) reject the null hypothesis that the observed distribution is not uniform
E) do nothing

Question 38

Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution. He collected a random sample and constructed the following frequency distribution to test his hypothesis: The observed value of chi-square for this goodness-of-fit test is ___.

A) 0.73
B) 6.72
C) 3.15
D) 7.81
E) 9.87

Question 39

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

A) 8
B) 7
C) 6
D) 5
E) 4

Question 40

A market researcher is studying the use of coupons by consumers of varying ages. She classifies consumers into four age categories and counts the number of grocery store customers who use at least one coupon during check out. It is expected that data are uniformly distributed across the four age categories. The observed data results in frequencies of 22, 35, 32, and 21. Using $\alpha$ =.05, the critical chi?square value is ___.

A) 13.277
B) 15.086
C) 7.8147
D) 11.070
E) 15.546

Question 41

Use the following set of observed frequencies to test the independence of the two variables. Variable one has values of 'A' and 'B'; variable two has values of 'C', 'D', and 'E'. Using $\alpha$ = 0.05, the critical chi-square value is ___.

A) 9.488
B) 1.386
C) 8.991
D) 3.357
E) 5.991

Question 42

Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages. She wonders whether acceptance is influenced by children in the household. Her staff prepared the following contingency table from a random sample of 100 households: Using $\alpha$ =.05, the critical value of chi-square is ___.

A) 5.02
B) 3.84
C) 7.37
D) 6.09
E) 5.99

Question 43

Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages. She wonders whether acceptance is influenced by children in the household. Her staff prepared the following contingency table from a random sample of 100 households: Catherine's null hypothesis is ___.

A) "children in household" is not independent of "preferred package"
B) "children in household" is independent of "preferred package"
C) "children in household" is related to "preferred package"
D) "children in household" influences "preferred package"
E) "pump" is independent of "tube"

Question 44

Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages. She wonders whether acceptance is influenced by children in the household. Her staff prepared the following contingency table from a random sample of 100 households: Using $\alpha$ =.05, the observed value of chi-square is ___.

A) 5.28
B) 9.49
C) 13.19
D) 16.79
E) 18.79

Question 45

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

A) 20
B) 9
C) 7
D) 12
E) 19

Question 46

A recent national poll showed the reading habits of adults during the last 12 months: A poll in a small Maritime town shows the following percentages:
The null hypothesis is ___.

A) the poll in the small Maritime town is not based on a random sample
B) the poll in the small Maritime town is not accurate
C) the sample size for the poll in the Maritime town is not large enough
D) the distributions are equal
E) the poll in the small Maritime town is based on a random sample

Question 47

Use the following set of observed frequencies to test the independence of the two variables. Variable one has values of 'A' and 'B'; variable two has values of 'C', 'D', and 'E'. Using $\alpha$ = 0.05, the estimates of the expected frequency in row 1 (A) column 1 (C) when the two variables are independent is ___.

A) 9.6
B) 12
C) 16
D) 10
E) 20

Question 48

Sam Hill, Director of Media Research, is analyzing subscribers to the TravelWorld magazine. He wonders whether subscriptions are influenced by the head of household's highest degree earned. His staff prepared the following contingency table from a random sample of 300 households: Sam's null hypothesis is ___.

A) "head of household classification" is related to "subscribes"
B) "head of household classification" is not independent of "subscribes"
C) "head of household classification" is independent of "subscribes"
D) "head of household classification" influences "subscribes"
E) "clerical is not related to managerial"

Question 49

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 there for this problem?

A) 6
B) 5
C) 4
D) 3
E) 1

Question 50

Contingency tables should not be used with expected cell frequencies ___.

A) less than the number of rows
B) less than the number of columns
C) less than 5
D) less than 30
E) less than 50

Question 51

A travel agent believes that vacation destinations are independent of the region of the country that the vacationer resides. She has compiled a table with six vacation destinations and five regions throughout Canada. When applying a chi-square test of independence to this table, the number of degrees of freedom is ___.

A) 9
B) 20
C) 30
D) 11
E) 12

Question 52

Sam Hill, Director of Media Research, is analyzing subscribers to the TravelWorld magazine. He wonders whether subscriptions are influenced by the head of household's highest degree earned. His staff prepared the following contingency table from a random sample of 300 households: The observed value of chi-square is ___.

A) 5.99
B) 28.30
C) 32.35
D) 60.65
E) 50.78

Question 53

Sam Hill, Director of Media Research, is analyzing subscribers to the TravelWorld magazine. He wonders whether subscriptions are influenced by the head of household's highest degree earned. His staff prepared the following contingency table from a random sample of 300 households: Using $\alpha$ =.05, the appropriate decision is ___.

A) reject the null hypothesis and conclude the two variables are independent
B) do not reject the null hypothesis and conclude the two variables are independent
C) reject the null hypothesis and conclude the two variables are not independent
D) do not reject the null hypothesis and conclude the two variables are not independent
E) do nothing

Question 54

A market researcher believes that industry type is independent of the operating margin. He compiles a table with seven industry classifications and classifies operating margin into five levels. When applying a chi-square test of independence to this table, the number of degrees of freedom is ___.

A) 24
B) 35
C) 12
D) 10
E) 11

Question 55

Sam Hill, Director of Media Research, is analyzing subscribers to the TravelWorld magazine. He wonders whether subscriptions are influenced by the head of household's highest degree earned. His staff prepared the following contingency table from a random sample of 300 households: Using $\alpha$ =.05, the critical value of chi-square is ___.

A) 5.99
B) 3.84
C) 5.02
D) 7.37
E) 9.99

Question 56

A recent national poll showed the reading habits of adults during the last 12 months: A poll in a small Maritime town shows the following percentages:
Comparing the critical and observed values of the goodness-of-fit chi-squared statistic and $\alpha$ = 0.05, the appropriate decision is ___.

A) reject the null hypothesis that the two distributions are equal
B) fail to reject the null hypothesis that the two distributions are unequal
C) reject the null hypothesis that the two distributions are unequal
D) fail to reject the null hypothesis that the two distributions are equal
E) reject the null hypothesis that the sample size for the smaller poll is large enough

Question 57

Use the following set of observed frequencies to test the independence of the two variables. Variable one has values of 'A' and 'B'; variable two has values of 'C', 'D', and 'E'. Using $\alpha$ = 0.05, the observed chi-square value is ___.

A) 0
B) 0.69
C) 1.54
D) 21.28
E) 8.29

Question 58

A recent national poll showed the reading habits of adults during the last 12 months: A poll in a small Maritime town shows the following percentages:
The observed chi-squared statistic is ___.

A) 5.14
B) 5.28
C) 6.14
D) 6.28
E) 6.54

Question 59

A recent national poll showed the reading habits of adults during the last 12 months: A poll in a small Maritime town shows the following percentages:
The critical value of the chi-squared goodness-of-fit statistic is ___.

A) 9.49
B) 7.82
C) 5.99
D) 5.82
E) 5.49

Question 60

Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages. She wonders whether acceptance is influenced by children in the household. Her staff prepared the following contingency table from a random sample of 100 households: Using $\alpha$ =.05, the appropriate decision is ___.

A) reject the null hypothesis and conclude the two variables are not independent
B) do not reject the null hypothesis and conclude the two variables are not independent
C) reject the null hypothesis and conclude the two variables are independent
D) do not reject the null hypothesis and conclude the two variables are independent
E) do nothing

Question 61

A market researcher is interested in determining whether the age of listeners influences their preferred musical styles. The following is a contingency table from a random sample of 385 individuals: The researcher uses $\alpha$ = 0.05. The critical chi-square value is ___.

A) 9.8
B) 10.9
C) 12.6
D) 15.5
E) 18.7

Question 62

A gasoline distributor wonders whether an individual's income level influences the grade of gasoline purchased. The following is a contingency table from a random sample of 300 individuals: The estimate of the expected number of individuals with income less than $30,000 who purchase regular gasoline when income and type of gasoline are independent is ___.

A) 60
B) 90
C) 120
D)80
E) 100

Question 63

Anita Cruz recently assumed responsibility for a large investment portfolio. She wonders whether industry sector influences investment objective. Her staff prepared the following contingency table from a random sample of 200 common stocks: Anita's null hypothesis is ___.

A) "investment objective" is related to "industry sector"
B) "investment objective" influences "industry sector"
C) "investment objective" is not independent of "industry sector"
D) "investment objective" is independent of "industry sector"
E) "growth" and "income" are independent

Question 64

A gasoline distributor wonders whether an individual's income level influences the grade of gasoline purchased. The following is a contingency table from a random sample of 300 individuals: The null hypothesis is ___.

A) "income" is independent of "type of gasoline"
B) "income" influences "type of gasoline"
C) "income" is not independent of "type of gasoline"
D) "income" is related to "type of gasoline"
E) "regular" is independent of "premium"

Question 65

Anita Cruz recently assumed responsibility for a large investment portfolio. She wonders whether industry sector influences investment objective. Her staff prepared the following contingency table from a random sample of 200 common stocks: Using $\alpha$ =.01, appropriate decision is ___.

A) reject the null hypothesis and conclude the two variables are not independent
B) reject the null hypothesis and conclude the two variables are independent
C) do not reject the null hypothesis and conclude the two variables are not independent
D) do not reject the null hypothesis and conclude the two variables are independent
E) do nothing

Question 66

A market researcher is interested in determining whether the age of listeners influences their preferred musical styles. The following is a contingency table from a random sample of 385 individuals: The researcher uses $\alpha$ = 0.05. The observed chi-square value is ___.

A) 86.59
B) 88.64
C) 89.59
D) 89.64
E) 90.59

Question 67

A gasoline distributor wonders whether an individual's income level influences the grade of gasoline purchased. The following is a contingency table from a random sample of 300 individuals: Using $\alpha$ =.05, appropriate decision is ___.

A) reject the null hypothesis and conclude the two variables are not independent
B) reject the null hypothesis and conclude the two variables are independent
C) do not reject the null hypothesis and conclude the two variables are not independent
D) do not reject the null hypothesis and conclude the two variables are independent
E) do nothing

Question 68

A gasoline distributor wonders whether an individual's income level influences the grade of gasoline purchased. The following is a contingency table from a random sample of 300 individuals: Using $\alpha$ =.05, observed chi-square value is ___.

A) 15.79
B) 4.44
C) 32.89
D) 51.79
E) 5.79

Question 69

Anita Cruz recently assumed responsibility for a large investment portfolio. She wonders whether industry sector influences investment objective. Her staff prepared the following contingency table from a random sample of 200 common stocks: Using $\alpha$ =.05, critical chi-square value is ___.

A) 9.21
B) 7.88
C) 15.09
D) 5.99
E) 7.89

Question 70

A gasoline distributor wonders whether an individual's income level influences the grade of gasoline purchased. The following is a contingency table from a random sample of 300 individuals: Using $\alpha$ =.01, critical chi-square value is ___.

A) 15.09
B) 7.88
C) 9.21
D) 16.81
E) 17.89

Question 71

A survey was conducted to determine the voting intentions of student in a large university. The percent of student who would definitely vote, likely vote, uncertain or will not vote are as follows:
Suppose 500 students were asked their intentions and gave the following responses:
At the 5% significance level, determine whether there is a significant difference in the voting intentions of students.

Question 72

A gasoline distributor wonders whether an individual's income level influences the grade of gasoline purchased. The following is a contingency table from a random sample of 300 individuals: Using $\alpha$ =.01, observed chi-square value is ___.

A) 24.93
B) 4.44
C) 32.89
D) 51.79
E) 54.98

Question 73

Is there a relationship between studying and passing final exams? Fifty students were surveyed about their activities leading to the statistics final exam. The students indicated whether they studied or partied and also whether they passed or failed the statistics final exam. The results are shown in the table below:
At the 5% significance level, can it be concluded that final exam results are related to activities leading up to the exam?

Question 74

A market researcher is interested in determining whether the age of listeners influences their preferred musical styles. The following is a contingency table from a random sample of 385 individuals: The researcher uses $\alpha$ = 0.05. The appropriate decision is ___.

A) reject the null hypothesis and conclude the two variables are not independent
B) reject the null hypothesis and conclude the two variables are independent
C) do not reject the null hypothesis and conclude the two variables are not independent
D) do not reject the null hypothesis and conclude the two variables are independent
E) do nothing

Question 75

Anita Cruz recently assumed responsibility for a large investment portfolio. She wonders whether industry sector influences investment objective. Her staff prepared the following contingency table from a random sample of 200 common stocks: Using $\alpha$ =.01, critical chi-square value is ___.

A) 9.21
B) 7.88
C) 15.09
D) 16.81
E) 18.81

Question 76

A gasoline distributor wonders whether an individual's income level influences the grade of gasoline purchased. The following is a contingency table from a random sample of 300 individuals: Using $\alpha$ =.05, critical chi-square value is ___.

A) 15.09
B) 5.99
C) 9.21
D) 16.81
E) 23.87

Question 77

A market researcher is interested in determining whether the age of listeners influences their preferred musical styles. The following is a contingency table from a random sample of 385 individuals: The researcher uses $\alpha$ = 0.05. The number of degrees of freedom is ___.

A) 12
B) 11
C) 10
D) 9
E) 6

Question 78

Anita Cruz recently assumed responsibility for a large investment portfolio. She wonders whether industry sector influences investment objective. Her staff prepared the following contingency table from a random sample of 200 common stocks: Using $\alpha$ =.01, observed chi-square value is ___.

A) 24.93
B) 8.17
C) 32.89
D) 6.59
E) 4.89