Deck 13: Goodness-Of-Fit Tests and Contingency Analysis

Question 1

If any of the observed frequencies are smaller than 5, then categories should be combined until all observed frequencies are at least 5.

Answer 1

False

Question 2

A business with 5 copy machines keeps track of how many copy machines need service on a given day. It believes this is binomially distributed with a probability of p = 0.2 of each machine needing service on any given day. It has collected the following based on a random sample of 100 days. Given this information, assuming that all expected values are sufficiently large to use the classes as shown above, the critical value for testing the hypothesis will be based on 5 degrees of freedom.

Answer 2

False

Question 3

It is believed that the number of drivers who are ticketed for speeding on a particular stretch of highway is a Poisson distribution with a mean of 3.5 per hour. A random sample of 100 hours is selected with the following results: Given this information, and without regard to whether there is a need to combine cells due to expected cell frequencies, the critical value for testing whether the distribution is Poisson with a mean of 3.5 per hour at an alpha level of .05 is x2 = 15.5073.

Answer 3

False

Question 4

A lube and oil change business believes that the number of cars that arrive for service is the same each day of the week. If the business is open six days a week (Monday - Saturday) and a random sample of n = 200 customers is selected, the expected number that will arrive on Monday is about 33.33.

Question 5

When the expected cell frequencies are smaller than 5, the cells should be combined in a meaningful way such that the expected cell frequencies do exceed 5.

Question 6

If the test statistic for a chi-square goodness-of-fit test is larger than the critical value, the null hypothesis should be rejected.

Question 7

A sample size of at least 30 is sufficient in most cases provided that none of the expected frequencies are less than 5.

Question 8

The goodness-of-fit test is always a one-tail test with the rejection region in the lower tail.

Question 9

A goodness-of-fit test can be used to determine whether a set of sample data comes from a specific hypothesized population distribution.

Question 10

In a goodness-of-fit test, when the null hypothesis is true, the expected value for the chi-square test statistic is < zero.

Question 11

The logic behind the chi-square goodness-of-fit test is based on determining how far the actual observed frequencies are from the expected frequencies.

Question 12

A business with 5 copy machines keeps track of how many copy machines need service on a given day. It believes this is binomially distributed with a probability of p = 0.2 of each machine needing service on any given day. It has collected the following based on a random sample of 100 days. Given this information, assuming that all expected values are sufficiently large to use the classes as shown above, the critical value based on a 0.05 level of significance is 9.4877.

Question 13

The Conrad Real Estate Company recently conducted a statistical test to determine whether the number of days that homes are on the market prior to selling is normally distributed with a mean equal to 50 days and a standard deviation equal to 10 days. The sample of 200 homes was divided into 8 groups to form a grouped data frequency distribution. If a chi-square goodness-of-fit test is to be conducted using an alpha = .05, the critical value is 14.0671.

Question 14

The Conrad Real Estate Company recently conducted a statistical test to determine whether the number of days that homes are on the market prior to selling is normally distributed with a mean equal to 50 days and a standard deviation equal to 10 days. The sample of 200 homes was divided into 8 groups to form a grouped data frequency distribution. The degrees of freedom for the test will be 7.

Question 15

A lube and oil change business believes that the number of cars that arrive for service is the same each day of the week. If the business is open six days a week (Monday - Saturday) and a random sample of n = 200 customers is selected, the critical value for testing the hypothesis using a goodness-of-fit test is x2 = 9.2363 if the alpha level for the test is set at .10.

Question 16

By combining cells we guard against having an inflated test statistic that could have led us to incorrectly accept the null hypothesis.

Question 17

If the sample size is large, the standard normal distribution can be used in place of the chi-square in a goodness-of-fit test for testing whether the population is normally distributed.

Question 18

It is believed that the number of drivers who are ticketed for speeding on a particular stretch of highway is a Poisson distribution with a mean of 3.5 per hour. A random sample of 100 hours is selected with the following results: Given this information, it can be seen that the cells will need to be combined since the actual number of occurrences at some levels of x is less than 5.

Question 19

A business with 5 copy machines keeps track of how many copy machines need service on a given day. It believes this is binomially distributed with a probability of p = 0.2 of each machine needing service on any given day. It has collected the following based on a random sample of 100 days. Given this information the expected number of days on which exactly 1 machine breaks down is 40.96.

Question 20

A lube and oil change business believes that the number of cars that arrive for service is the same each day of the week. If the business is open six days a week (Monday - Saturday) and a random sample of n = 200 customers is selected, the sum of the expected frequencies over the six days cannot be determined without seeing the actual sample data.

Question 21

By combining cells we guard against having an inflated test statistic that could have led us to incorrectly reject the H0.

Question 22

The goodness-of-fit test is essentially determining if the test statistic is significantly larger than zero.

Question 23

Contingency analysis is used only for numerical data.

Question 24

If the calculated chi-square statistic for specific degrees of freedom is a large value, this supports evidence that the fit of the actual data to the hypothesized distribution is not good, and HA should be rejected.

Question 25

A study was recently conducted in which people were asked to indicate which news medium was their preferred choice for national news. The following data were observed: Given this data, if we wish to test whether the preferred news source is independent of age with an alpha equal to .05, the critical value will be a chi-square value with 9 degrees of freedom.

Question 26

A survey was recently conducted in which males and females were asked whether they owned a laptop personal computer. The following data were observed: Given this information, the sample size in the survey was 300 people.

Question 27

In conducting a test of independence for a contingency table that has 4 rows and 3 columns, the number of degrees of freedom is 11.

Question 28

If one or more parameters are left unspecified in a goodness-of-fit test, they must be estimated from the sample data and one degree of freedom is lost for each parameter that must be estimated.

Question 29

A study was recently conducted in which people were asked to indicate which new medium was their preferred choice for national news. The following data were observed: Given this data, if we wish to test whether the preferred news source is independent of age, the expected frequency in the cell, radio-under 21 cell is 30.

Question 30

A survey was recently conducted in which males and females were asked whether they owned a laptop personal computer. The following data were observed: Given this information, if having a laptop is independent of gender, the expected number of males with laptops in this survey is 150.

Question 31

A survey was recently conducted in which males and females were asked whether they owned a laptop personal computer. The following data were observed: Given this information, if an alpha level of .05 is used, the sum of the expected cell frequencies will be equal to the sum of the observed cell frequencies.

Question 32

A study was recently conducted in which people were asked to indicate which news medium was their preferred choice for national news. The following data were observed: Given this data, if we wish to test whether the preferred news source is independent of age, the cell with the largest expected cell frequency is also the cell with the largest observed frequency.

Question 33

The sampling distribution for a goodness-of-fit test is the Poisson distribution.

Question 34

When the variables of interest are both categorical and the decision maker is interested in determining whether a relationship exists between the two, a statistical technique known as contingency analysis is useful.

Question 35

Contingency analysis helps to make decisions when multiple proportions are involved.

Question 36

A survey was recently conducted in which males and females were asked whether they owned a laptop personal computer. The following data were observed: Given this information, if an alpha level of .05 is used, the critical value for testing whether the two variables are independent is x2 = 3.8415.

Question 37

Managers use contingency analysis to determine whether two categorical variables are independent of each other.

Question 38

A survey was recently conducted in which males and females were asked whether they owned a laptop personal computer. The following data were observed: Given this information, if an alpha level of .05 is used, the test statistic for determining whether having a laptop is independent of gender is approximately 14.23.

Question 39

A goodness-of-fit test can decide whether a set of data comes from a specific hypothesized distribution.

Question 40

A cell phone company wants to determine if the use of text messaging is independent of age. The follow data has been collected from a random sample of their customers. Using the data above, in order to test for the independence of age and the use of text messaging, the expected value for the "under 21 and regularly use text messaging" cell is 82.

Question 41

If a contingency analysis test is performed with a 4 × 6 design, and if alpha = .05, the critical value from the chi-square distribution is 24.9958

Question 42

A study was recently done in the United States in which car owners were asked to indicate whether their most recent car purchase was a U.S. car, a German car, or a Japanese car. The people in the survey were divided by geographic region in the United States. The following data were recorded. Given this situation, to test whether the car origin is independent of the geographical location of the buyer, the sum of the expected cell frequencies will equal 1,240.

Question 43

A study was recently done in the United States in which car owners were asked to indicate whether their most recent car purchase was a U.S. car, a German car, or a Japanese car. The people in the survey were divided by geographic region in the United States. The following data were recorded. Given this situation, the null hypothesis to be tested is that the car origin is dependent on the geographical location of the buyer.

Question 44

A cell phone company wants to determine if the use of text messaging is independent of age. The following data has been collected from a random sample of customers. Using this data, if we wish to test whether the preferred news source is independent of age using a 0.05 level of significance, the critical value is 5.9915.

Question 45

In a contingency analysis, we expect the actual frequencies in each cell to approximately match the corresponding expected cell frequencies when H0 is true.

Question 46

A study was recently conducted in which people were asked to indicate which news medium was their preferred choice for national news. The following data were observed: Given this data, if we wish to test whether the preferred news source is independent of age, for an alpha = .05 level, the critical value from the chi-square table is based on 8 degrees of freedom.

Question 47

In a contingency analysis the expected values are based on the assumption that the two variables are independent of each other.

Question 48

In a chi-square contingency test, the number of degrees of freedom is equal to the number of cells minus 1.

Question 49

A cell phone company wants to determine if the use of text messaging is independent of age. The following data has been collected from a random sample of customers. To conduct a test of independence, the difference expected value for the "40 and over and regularly use text messaging" cell is just over 43 people.

Question 50

Contingency analysis can be used when the level of data measurement is nominal or ordinal.

Question 51

A study was recently done in the United States in which car owners were asked to indicate whether their most recent car purchase was a U.S. car, a German car, or a Japanese car. The people in the survey were divided by geographic region in the United States. The following data were recorded. Given this situation, to test whether the car origin is independent of the geographical location of the buyer, the expected number of people in the sample who bought a German made car and who lived on the East Coast is just under 40 people.

Question 52

Unlike the case of goodness-of-fit testing, with contingency analysis there is no restriction on the minimum size for an expected cell frequency.

Question 53

A contingency table and a cross-tabulation table are two separate things and should not be used for the same purpose.

Question 54

In a chi-square contingency analysis application, the expected cell frequencies will be equal in all cells if the null hypothesis is true.

Question 55

A study was recently done in the United States in which car owners were asked to indicate whether their most recent car purchase was a U.S. car, a German car, or a Japanese car. The people in the survey were divided by geographic region in the United States. The following data were recorded. Given this situation, the sample size used in this study was nine.

Question 56

To employ contingency analysis, we set up a 2-dimensional table called a contingency table.

Question 57

A study was recently conducted in which people were asked to indicate which news medium was their preferred choice for national news. The following data were observed: Given this data, if we wish to test whether the preferred news source is independent of age, for an alpha = .05 level, the critical value from the chi-square table is 9.4877.

Question 58

A study was recently conducted in which people were asked to indicate which news medium was their preferred choice for national news. The following data were observed: Given this data, if we wish to test whether the preferred news source is independent of age, for an alpha = .05 level, the test statistic is computed to be approximately 40.70.

Question 59

A study was recently done in the United States in which car owners were asked to indicate whether their most recent car purchase was a U.S. car, a German car, or a Japanese car. The people in the survey were divided by geographic region in the United States. The following data were recorded. Given this situation, to test whether the car origin is independent of the geographical location of the buyer, the critical value for alpha = .10 is 14.6837.

Question 60

In order to apply the chi-square contingency methodology for quantitative variables, we must first break the quantitative variable down into discrete categories.

Question 61

If a sample with n = 30 subjects distributed over 5 categories was selected, a chi-square test for goodness-of-fit will be used. How many degrees of freedom will be used in determining the chi-square test statistic?

A) 3
B) 4
C) 5
D) 25

Question 62

A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days. To conduct a goodness-of-fit test, what is the expected value for Friday?

A) 20
B) 25
C) 16
D) 100

Question 63

We are interested in determining whether the opinions of the individuals on gun control (as to Yes, No, and No Opinion) are uniformly distributed. A sample of 150 was taken and the following data were obtained. The conclusion of the test with alpha = 0.05 is that the views of people on gun control are:

A) uniformly distributed.
B) not uniformly distributed.
C) inconclusive.
D) None of the above

Question 64

Which of the following statements is true in the context of a chi-square goodness-of-fit test?

A) The degrees of freedom for determining the critical value will be the number of categories minus 1.
B) The critical value will come from the standard normal table if the sample size exceeds 30.
C) The null hypothesis will be rejected for a small value of the test statistic.
D) A very large test statistic will result in the null not being rejected.

Question 65

What does the term observed cell frequencies refer to?

A) The frequencies found in the population being examined
B) The frequencies found in the sample being examined
C) The frequencies computed from H0
D) The frequencies computed from H1

Question 66

In a chi-square goodness-of-fit test, by combining cells we guard against having an inflated test statistic that could have caused us to:

A) incorrectly reject the H0.
B) incorrectly accept the H0.
C) incorrectly reject the H1.
D) incorrectly accept the H1.

Question 67

What does the term expected cell frequencies refer to?

A) The frequencies found in the population being examined
B) The frequencies found in the sample being examined
C) The frequencies computed from H0
D) the frequencies computed from H1

Question 68

To use contingency analysis for numerical data, which of the following is true?

A) Contingency analysis cannot be used for numerical data.
B) Numerical data must be broken up into specific categories.
C) Contingency analysis can be used for numerical data only if both variables are numerical.
D) Contingency analysis can be used for numerical data only if it is interval data.

Question 69

We expect the actual frequencies in each cell to approximately match the corresponding expected cell frequencies when:

A) H0 is false.
B) H0 is true.
C) H0 is falsely accepted.
D) the variables are related to each other.

Question 70

If a contingency analysis test performed with a 4 × 6 design results in a test statistic value of 18.72, and if alpha = .05, the null hypothesis that the row and column variable are independent should be rejected.

Question 71

A chi-square test for goodness-of-fit is used to test whether or not there are any preferences among 3 brands of peas. If the study uses a sample of n = 60 subjects, then the expected frequency for each category would be:

A) 20
B) 30
C) 60
D) 33

Question 72

Consider a goodness-of-fit test with a computed value of chi-square = 27.385 and a critical value = 13.388, the appropriate conclusion would be to:

A) reject H0.
B) fail to reject H0.
C) reject HA.
D) take a larger sample.

Question 73

A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days. Assuming that a goodness-of-fit test is to be conducted using a 0.10 level of significance, the critical value is:

A) 9.4877
B) 11.0705
C) 7.7794
D) 9.2363

Question 74

If the null hypothesis is not rejected, you do not need to worry when the expected cell frequencies drop below 5.0

Question 75

The degrees of freedom for the chi-square goodness-of-fit test are equal to ________, where k is the number of categories.

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

Question 76

A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days. Based on this information how many degrees for freedom are involved in this goodness of fit test?

A) 99
B) 100
C) 4
D) 5

Question 77

A researcher is using a chi-square test to determine whether there are any preferences among 4 brands of orange juice. With alpha = 0.05 and n = 30, the critical region for the hypothesis test would have a boundary of:

A) 7.81
B) 8.71
C) 8.17
D) 42.25

Question 78

A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days. What is the value of the test statistic needed to conduct a goodness-of-fit test?

A) 8.75
B) 7.7794
C) 2.46
D) 2.50

Question 79

A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days. Based on these data, conduct a goodness-of-fit test using a 0.10 level of significance. Which conclusion is correct?

A) Arrivals are not uniformly distributed over the weekday because (test statistic) > (critical value).
B) Arrivals are uniformly distributed over the weekday because (test statistic) > (critical value).
C) Arrivals are not uniformly distributed over the weekday because (test statistic) < (critical value).
D) Arrives are uniformly distributed over the weekday because (test statistic) < (critical value).

Question 80

In a goodness-of-fit test about a population distribution, if one or more parameters are left unspecified in H0, they must be estimated from the sample data. This will reduce the degrees of freedom by ________ for each estimated parameter.

A) 1
B) 2
C) 3
D) None of the above