Ch. 15
Identify which of the examples would be appropriate for a chi-square test for independence.
A lawyer wants to show whether or not gender and the ability to be promoted are related and a researcher wants to determine whether or not the race of a driver will influence whether a police officer will search a vehicle, once stopped.
A contingency table shows frequencies for ____________ or ___________ variables
Categorical; ordinal
A rule known as _________________ Rule requires that each cell have a frequency greater than five.
Cochran's
A _____________ table is used to summarize ____________ frequencies from customer surveys or designed experiments.
Contingency; response
A Poisson distribution has which of the following characteristics?
Describes a nonnegative integer value. Often called the model for rare events because the average is typically a small value. Describes events that occur independently of each other.
The acronym ECDF stands for ___________ ____________ distribution function.
Empirical Cumulative
True or false: When testing a population distribution using a goodness-of-fit test one should let a software package find the best distribution.
False
There are many alternatives to the chi-square test for goodness-of-fit. Which of the tests below is NOT a goodness-of-fit test?
Gilbey-Tanqiers
Which of the null hypotheses would be correct for a Poisson goodness-of-fit test?
H0: The number of arrivals at a fast food counter between noon and 1 pm follow a Poisson distribution.
The hypotheses for the chi-square test for independence are
H0: The two variables are independent. H1: The two variables are not independent.
A researcher would like to test the assumption that a particular brand of laundry detergent is twice as popular as the two next best selling brands which she believes have equal popularity. The researcher conducts an experiment with a focus group to determine the proportion of times each of the brands is selected. The null hypothesis would be:
H0: π1 = .5, π2 = .25, π3 = .25
A candy company claims that the proportion of red, green, and yellow jelly beans in a bag is 0.3, 0.4, and 0.3. Which of the following is the correct set of hypotheses for testing the company's claim?
Ho: πred = 0.3 πgreen = 0.4 πyellow = 0.3; H1: At least one of the π's is different from its hypothesized value.
In the chi-square test for independence, the null hypothesis assumes two categorical variables are independent. If the variables are independent then the contingency table ________________ frequencies should be close in value to the ____________ frequencies
Observed; expected
Identify which are common distributions tested using the chi-square goodness-of-ft.
Poisson Normal Uniform
Match the degrees of freedom to the test.
Poisson goodness-of-fit with λ specified a priori matches df = c - 1 Poisson goodness-of-fit with λ estimated from the sample df = c - 1 -1 Uniform goodness of fit test df = c - 1
Which of the following is NOT an example of a multinomial distribution?
The probability that an exam can be completed in less than 30 minutes is 1-e-λ30
Identify the reasons why one might analyze quantitative data using a contingency table.
The researcher might not want to make an assumption about a mathematical form for the relationship between X and Y; The assumption of a normal distribution, required for regression, might be invalid; The researcher might have a mixture of quantitative and qualitative variables.
True or false: A quantitative variable might be included in a contingency table when the second variable is categorical.
True
True or false: Open-ended classes are acceptable in contingency tables.
True
True or false: The advantage of using the equal frequency method for a normal goodness-of-fit test is that the expected frequencies will not be too small.
True
A normal distribution is a reasonable assumption if the sample data
are not badly skewed and show a reasonable degree of central tendency.
A _______________________ distribution can create a mixtures problem where it is difficult to identify an underlying distribution
bimodal
A random sample of customer monthly accounts from a department store are tested for goodness-of-fit to a normal distribution. The sample shows that xx = $155 and s = $25. The test resulted in χ2calc = 4.86 with p-value = .089. Given that α = .05, we would
conclude that the distribution can be assumed normal.
Examples of Poisson data generating situations include
defects on automobile paint jobs. occurrence of new flu cases each day. queuing systems.
The expected frequency for each cell in a contingency table is calculated using the formula
ejk = RjCk/n
For a uniform GOF test, we need to for c bins of ______________ width
equal
A simple visual inspection of a histogram or dot plot is often called an _______________ test
eyeball
True or false: Only multinomial distributions can be tested using a GOF Test.
false
When grouping raw data for a uniform goodness-of-fit test we must define our own ranges by creating a ________________ distribution
frequency
When testing for a Poisson model, if the population average is unknown one should estimate λ
from the sample.
The classes used for a Poisson goodness-of-fit test will always include an open-ended class on the ______________ end
high
Often, an initial inspection of a ________________ can help one eliminate a possible distribution from consideration before conducting a formal goodness-of-fit test.
histogram
When stating the null hypothesis for a Chi-square test of independence, the null hypothesis always assumes the two variables are
independent
Each probability distribution has its own ______________ about the underlying process.
logic
When a sample has been created by taking observations from two distinct populations, the underlying distribution can be difficult to ascertain. This is called a
mixtures problem.
Bins for GOF tests do not have to be equal width and can be
open ended
A contingency table shows frequencies for ___________ or ___________ variables
ordinal; categorical
Small expected frequencies can create a problem for a chi-square test because small samples lack
power
For a 2x2 contingency table, testing for independence with the chi-square test is the same as conducting a z test comparing two
proportions
The degrees of freedom in a Chi-square distribution is (____________ -) x (_________ -1)
r; c
For the Poisson goodness-of-fit test, the expected frequencies are calculated by multiplying P(X = x) by the
sample size
Quantitative variables can be analyzed using contingency tables by
summarizing frequencies into bins and using the bins as categories.
Small expected frequencies can create a problem for a chi-square test because
they inflate the value of the chi-square statistic because ej is in the denominator.
Normal goodness-of-fit tests require ______________ parameters that can be specified a priori or _____________ from the sample
two; estimated
A random sample of customer monthly accounts for a specific department store have xx = $155 and s = $25. We want to determine whether individual customer accounts are consistent with a random sample from a normal distribution. The sample resulted in a χ2calc = 4.86 with a p-value = .089. If α = .05
we would conclude that the distribution on monthly accounts in normal.
Examples of natural groupings for data would be
weeks. US states. days.
For a 2x2 contingency table, testing for independence with the chi-square test is the same as conducting a __________________ test comparing two proportions.
z
The chi-square distribution has which of the following characteristics:
χ2 critical is dependent on degrees of freedom = (r-1)(c-1) and χ2 is never negative.
A multinomial distribution has k probabilities that sum to
1
When conducting a normal goodness-of-fit test with 6 bins and estimating the mean and standard deviation from the sample, the degrees of freedom would be
3
The test for independence for a contingency table is unreliable when the expected frequencies in each cell are less than or equal to
5
When performing a GOF test for a Poisson distribution assuming λ = 3 and 6 classes, the d.f. would be
5
