Chapter 12: Analysis of Categorial Data 1

CHAPTER TWELVE
Analysis of Categorical Data
1. In a chi-square goodness-of-fit test, theoretical frequencies are also called _______ frequencies.
A. actual
B. expected C. empirical D. observed

2. In a chi-square goodness-of-fit test, actual frequencies are also called _______ frequencies.
A. calculated
B. expected C. theoretical D. observed

3. The number of degrees of freedom in a chi-square goodness of fit test is _______.

A. the number of categories
B. the number of categories minus 1
C. the number of categories minus the number of parameters estimated
D. the number of categories minus the number of parameters estimated minus 1

4. A chi-square goodness-of-fit test is to be used to determine if a distribution is normally distributed.

The data will be divided into "k" categories. Both the mean and standard deviation must be
estimated. The degrees of freedom would be _______.
A. k-1
B. k-2 C. k-3 D. k-4

5. The decision rule in a chi-square goodness of fit test is to reject the null hypothesis if _______.
A. the computed chi-square is less than the table chi-square
B. the computed chi-square is greater than the table chi-square
C. the computed chi-square is greater than zero
D. the computed chi-square is greater than the number of categories

6. When using the chi-square goodness-of-fit test, a statistician needs to make certain that none of the
expected frequencies are less than _______.
A. the number of categories
B. 30 C. 5 D. 0

7. A chi-square goodness-of-fit test is being used to determine if the observed frequencies from seven
categories are significantly different from the expected frequencies from the seven categories. No
parameters are estimated from the data. Using Alpha = 0.05, the degrees of freedom for this test
are _______.
A. 7 B. 6 C. 5 D. 0

8. A chi-square goodness-of-fit test is being used to determine if the observed frequencies from seven
categories are significantly different from the expected frequencies from the seven categories. No
parameters are estimated from the data. Using Alpha = 0.05, the critical chi-square value is _______.
A. 2.204
B. 11.070 C. 12.592 D. 14.067
9. A chi-square goodness of fit test is to be performed. The degrees of freedom are 12, and alpha is 0.10.
The table chi-square value that defines the rejection region is _______.
A. 26.217
B. 6.304
C. 18.549 D. 17.275

10. A chi-square goodness of fit test is to be performed. The degrees of freedom are 17, and alpha is 0.01.
The table chi-square value that defines the rejection region is _______.
A. 33.409 B. 24.769 C. 10.085 D. 30.995
CHAPTER ELEVEN
Analysis of Variance and Design of Experiments

1. If a researcher wants to conduct a test about the differences in the means for more than two
independent populations, she can use _______.
A. the related samples t-test B. analysis of variance
C. a confidence interval D. the multiple population t-test

2. Analysis of variance tests use the _______.

A. t distribution B. normal distribution C. F distribution D. exponential distribution

3. The statistical methods of analysis of variance assume _____________.

A. normally distributed populations B. binomially distributed populations
C. uniformly distributed populations D. exponentially distributed populations

4. The statistical methods of analysis of variance assume _____________.

A. convenience samples B. judgment samples C. random samplesD. quota samples

5. The statistical methods of analysis of variance assume ______________.

A. equal sample means B. equal population variances
C. equal population proportions D. equal sample proportions

6. In designed experiments for analysis of variance, the dependent variable is also called the ____________.
A. classification variable B. blocking variable
C. concomitant variable D. response variable

7. In designed experiments for analysis of variance, independent variables are also called _____________.
A. response variables B. factors C. cofactors D. mitigating variables

8. Determining the table value for the F distribution is different from finding values in the t distribution
tables because the F table requires _____ values for degrees of freedom.
A. one B. two C. three D. more than three

9. An experimental design contains _____________.

A. only independent variables B. only dependent variables
C. neither independent or dependent variables D. both independent and dependent
variables
 Chapter 12: Analysis of Categorial Data 3

10. In experimental design, a variable that the experimenter controls or modifies in the experiment is
called a _____________.
A. classification variableB. treatment variable C. dummy variable D. response variable

CHAPTER TEN
Statistical Inferences about Two Populations

1. Assume that two independent random samples of size 100 each are taken from a population that has
a variance of 36. What is the probability that the difference in the sample means is greater than 1?
A. 0.1190 B. 0.3810 C. 0.7200 D. 0.3600

2. Assume that two independent random samples of size 100 each are taken from a population that has
a variance of 36. What is the probability that the difference in the sample means is less than 2?
A. 0.4909 B. 0.9909 C. 0.0091 D. 0.5091

3. A researcher is performing a two-tailed related samples (matched pairs) t-test. A total of 12 people
are in the sample, and before and after measures are taken. The observed t value for this is
-1.84. The level of significance is 0.05. The correct decision is to _______.
A. do not reject the null hypothesis B. reject the null hypothesis
C. take a larger sample D. use the z table instead of the t table

4. A researcher is performing a two-tailed related samples (matched pairs) t-test. A total of 8 people are
in the sample, and before and after measures are taken. The observed t value for this is
-1.97. The level of significance is 0.10. The correct decision is to _______.
A. do not reject the null hypothesis B. reject the null hypothesis
C. take a larger sample D. use the z table instead of the t table

5. Suppose that .06 of each of two populations possess a given characteristic. Samples of size 400 are
randomly drawn from each population. The probability that the difference between the
first sample proportion which possess the given characteristic and the second sample
proportion which possess the given characteristic being more than +.03 is _______.
A. 0.4943 B. 0.9943 C. 0.0057 D. 0.5057

6. Suppose that .06 of each of two populations possess a given characteristic. Samples of size 400 are
randomly drawn from each population. The standard deviation for the sampling
distribution of differences between the first sample proportion and the second sample
proportion (used to calculate the z score) is _______.
A. 0.00300 B. 0.01200 C. 0.05640 D. 0.00014

7. Suppose that .06 of each of two populations possess a given characteristic. Samples of size 400 are
randomly drawn from each population. What is the probability that the differences in
sample proportions will be greater than 0.02?
A. 0.4535 B. 0.9535 C. 0.0465 D. 0.5465

8. If you are testing a hypothesis that two population proportions are the same, you _______.
A. should calculate a "pooled" value for the sample proportion
 B. should not calculate a "pooled" value for the sample proportion
C. use a sample proportion of zero
D. always use a 0.05 level of significance

9. A researcher is interested in estimating the difference in two population proportions. A sample of 400
from each population results in sample proportions of .61 and .64. The point estimate of
the difference in the population proportions is _______.
A. -0.03 B. 0.625 C. 0 D. 0.400

10. A researcher is interested in estimating the difference in two population proportions. A sample of 400
from each population results in sample proportions of .61 and .64. A 90% confidence
interval for the difference in the population proportions is _______.
A. -0.10 to 0.04 B. -0.09 to 0.03 C. -0.11 to 0.05 D. -0.07 to 0.01

CHAPTER NINE
Statistical Inference: Hypothesis Testing for Single Populations

1. Hypothesis testing is derived from the mathematical notion of _______.

A. direct proof B. indirect proof C. margin of error D. infinity

2. The first step in testing a hypothesis is to establish _______.

A. an not rejectance hypothesis and a rejection hypothesis B. a power function
C. a null hypothesis and alternative hypothesis D. an indirect hypothesis

3. In testing hypotheses, the researcher initially assumes that the _______.

A. alternative hypothesis is true. B. null hypothesis is true
C. errors cannot be made D. the population parameter of interest is known

4. Consider the following null and alternative hypotheses.

Ho: s ³ 558 Ha: s < 558 These hypotheses _______________.
A. are not mutually exclusive B. are not collectively exhaustive
C. do not reference a population parameter D. are established correctly

5. The region of the distribution in hypothesis testing in which the null hypothesis is rejected is called
the _______.
A. not rejectance region B. null region C. alternative region D. rejection region

6. The rejection and not rejectance regions are divided by a point called the _______.
A. dividing point B. critical value C. rejection value D. not rejectance value

7. The portion of the distribution which is not in the rejection region is called the _______.
A. tolerable region B. not rejectance region C. null region D. alternative region

8. The probability of committing a Type I error is called _______.

A. the level of significance B. beta C. the power of the test D. reliability
 Chapter 12: Analysis of Categorial Data 5

9. In statistical hypothesis testing, another name for Alpha is _______.

A. level of significance B. power C. beta D. Type II error probability

10. When a true null hypothesis is rejected, the researcher has made a _______.
A. Type II error B. Type I error C. sampling error D. powerful error

CHAPTER EIGHT
Statistical Inference: Estimation for Single Populations

1. When a statistic calculated from sample data is used to estimate a population parameter, it is called __.
A. an interval estimate B. a point estimate C. a statistical parameter D. a good guess

2. When a range of values is used to estimate a population parameter, it is called _______.

A. an interval estimate B. a point estimate C. a statistical parameter D. a range estimate

3. The z value associated with a two-sided 90% confidence interval is _______.

A. 1.28 B. 1.645 C. 1.96 D. 2.575

4. The z value associated with a two-sided 80% confidence interval is _______.

A. 1.645 B. 1.28 C. 0.84 D. 0.29

5. Suppose a random sample of 36 is selected from a population with a standard deviation of 12. If the
sample mean is 98, the 99% confidence interval to estimate the population mean is _______.
A. 94.08 to 101.92 B. 92.85 to 103.15 C. 97.35 to 98.65 D. 93.34 to 102.66

6. In order to find values in the t distribution table, you must convert the sample size or sizes to _______.
A. population sizes B. degrees of freedom C. z values D. student values

7. If the degrees of freedom in a t distribution get very large, _______.

A. the t values and the z values are almost the same. B. the sample size must be very small
C. the population size must be very large D. the sample mean approaches zero

8. The table t value associated with 12 degrees of freedom and used to compute a 95% confidence
interval is _______.
A. 3.055 B. 2.179 C. 1.782 D. 1.796

9. In estimating sample size, if the population standard deviation is unknown, it can be estimated by
using _______.
A. the population mean B. one-fourth of the rangeC. one-half of the range D. the z score

10. In estimating the sample size necessary to estimate p, if there is no good approximation for the value
of p available, the value of ____ should be used as an estimate of p in the formula.
A. 0.10 B. 0.50 C. 0.40 D. 1.96
 CHAPTER SEVEN
Sampling and Sampling Distributions

1. Saving time and money are reasons to take a _______________ rather than a census.
A. poll B. sample C. profile D. Fishbone

2. Which of the following is NOT a reason for using a sample, rather than a census?
A. sampling saves time B. sampling saves money
C. some testing procedures are destructive D. some testing procedures are deductive

3. Which of the following is a random sampling technique?

A. judgment sampling B. systematic sampling C. quota sampling D. convenience sampling

4. Which of the following is a nonrandom sampling technique?

A. quota sampling B. systematic sampling C. cluster sampling D. stratified sampling

5. The directory or map from which a sample is taken is called the ______________.
A. population B. census C. profile D. frame

6. The two major categories of sampling methods are _________________.

A. quota and convenience B. random and nonrandom
C. stratified and cluster D. proportionate and disproportionate

7. If every unit of the population has the same probability of being selected to the sample, then the
researcher is probably conducting _______.
A. nonrandom sampling B. random sampling
C. judgment sampling D. equivalent sampling

8. The most elementary type of random sampling is _______.

A. stratified sampling B. simple random sampling
C. cluster sampling D. judgment sampling

9. With ______ random sampling, there is homogeneity within a subgroup or stratum.

A. judgmental B. simple C. cluster D. stratified

10. The standard deviation of a sampling distribution is commonly called _______.

A. statistical leverage. B. the uniform spread. C. statistical margin. D. the standard error.

CHAPTER SIX
Continuous Distributions

1. Which of the following is NOT a continuous distribution?

A. normal distribution B. exponential distribution
C. uniform distribution D. binomial distribution

2. The uniform distribution is _______________.

 Chapter 12: Analysis of Categorial Data 7

A. bimodal B. skewed to the right C. skewed to the left D. symmetric

3. The distribution in the following graph is a ________ distribution.

0.06
0.05
0.04

f(X )
0.03
0.02
0.01
0.00
35 40 45 50 55 60 x 65

A. normal B. gamma C. exponential D. uniform

4. The distribution in the following graph is a ________ distribution.

0.5

0.4

0.3

0.2

0.1

0
x

A. norma l B. gamma C. exponential D. uniform

5. The distribution in the following graph is a ________ distribution.

1.2
1.0
0.8
0.6
0.4
0.2
0.0
0 1 2 3 4 5 x 6

A. normal B. gamma C. exponential D. uniform

6. If x is uniformly distributed over the interval 8 to 12, inclusively (8 £ x £ 12), then the height of this
distribution, f(x), is __________________.
A. 1/8 B. ¼ C. 1/12 D. 1/20

7. If x is uniformly distributed over the interval 8 to 12, inclusively (8 £ x £ 12), then the P(9 £ x £ 11)
is?
A. 0.250 B. 0.500 C. 0.333 D. 1.000

8. If arrivals at a bank follow a Poisson distribution, then the time between arrivals would be _______.
A. normally distributed B. exponentially distributed
C. a binomial distribution D. equal to lambda

9. The exponential distribution is _______.

A. symmetric B. bimodal C. skewed to the left D. skewed to the right

10. The standard normal distribution is also called _______.

A. an exponential distribution B. the z distribution
C. a discrete distribution D. a finite distribution

CHAPTER FIVE
 Discrete Distributions

1. Variables which take on values only at certain points over a given interval are called _______.
A. point variables B. continuous random variables
C. discrete random variables D. value variables

2. The number of automobiles sold by a dealership in a day is an example of _______.

A. a discrete random variable B. a continuous random variable
C. the binomial distribution D. the normal distribution

3. The amount of time a patient waits in a doctor's office is an example of _________.

A. the normal distribution B. the binomial distribution
C. a discrete random variable D. a continuous random variable

4. A fair coin is tossed 5 times. What is the probability that exactly 2 heads are observed?
A. 0.313 B. 0.073 C. 0.400 D. 0.156

5. If x is a binomial random with n=8 and p=0.6, what is the probability that x is equal to 5?
A. 0.625 B. 0.279 C. 0.209 D. 0.300

6. If x is a binomial random with n=10 and p=0.4, what is the probability that x is less than 2?
A. 0.167 B. 0.046 C. 0.040 D. 0.006

7. Suppose a committee of 3 people is to be selected from a group consisting of 4 men and 5 women.
What is the probability that all three people selected are men?
A. 0.05 B. 0.33 C. 0.11 D. 0.80

8. Suppose a committee of 3 people is to be selected from a group consisting of 4 men and 5 women.
What is the probability that one man and two women are selected?
A. 0.15 B. 0.06 C. 0.33 D. 0.48

9. Using the binomial tables, if n=20 and p=.4 find P(x=7).

A. 0.166
B. 0.180 C. 0.002 D. 0.074

10. The Poisson distribution is being used to approximate a binomial distribution. If n=40 and p=0.06,
what value of lambda would be used?
A. 0.06 B. 2.4 C. 0.24 D. 24

CHAPTER FOUR
Probability

1. Which of the following is not a method of assigning probabilities?

A. classical probability B. relative frequency
C. subjective probability D. elementary inference

2. A process that produces outcomes is called _______.

A. an event B. an experiment C. a result D. population equivalent
 Chapter 12: Analysis of Categorial Data 9

3. The method of assigning probabilities based on rules and laws is called _______.
A. classical probability B. relative frequency
C. subjective probability D. elementary inference

4. An outcome of an experiment is called _______.

A. an event B. a priori elements C. a probability D. a complement

5. If an event is in the intersection of X and Y, then this event is _______.

A. not in the union of X and Y B. not in X C. not in Y D. in both X and Y

6. The joint probability of X and Y is also referred to as _______.

A. the intersection of X and Y B. the union of X and Y
C. the marginal probability of X and Y D. the probability of X given Y

7. Given P(A) = 0.40, P(B) = 0.50, P(A Ç B) = 0.15. Which of the following is true?
A. A and B are independent B. A and B are mutually exclusive
C. A and B are collectively exhaustive D. A and B are not independent

8. Given P(A) = 0.25, P(B) = 0.40, P(A Ç B) = 0.10. Find P(B|A).

A. 0.20 B. 0.50 C. 0.40 D. 0.65

9. There are three Democrats and four Republicans in a group of seven people. If two people are
selected from the total of seven, how many ways can two people be selected?
A. 12 B. 21 C. 14 D. 15

10. Given P(A) = 0.6, P(B) = 0.4, P(A|B)=0.50. Find P(A È B).
A. 1.00 B. 0.80 C. 1.10 D. 0.10

CHAPTER THREE
Descriptive Statistics

1. Statistical measures used to yield information about the middle of a group of numbers are called ____.
A. averages B. measures of variability C. measures of central tendency D. Z scores

2. Which of the following is NOT a measure of central tendency?

A. mean B. median C. variance D. mode

3. The lowest appropriate level of measurement for the mean is _________.

A. nominal B. ordinal C. interval D. ratio

4. The middle value in an ordered array of numbers is called the _______.

A. mode B. mean C. median D. coefficient of variation

5. The notation X usually refers to the _______________.

A. population standard deviation B. sample variance C. population mean D. sample mean
6. The average of the squared deviations from the arithmetic mean is called the _______.
A. standard deviation B. mean absolute deviation C. variance D. coefficient of variation

7. The lowest appropriate level of measurement for the Interquartile Range is _________.
A. nominal B. ordinal C. interval D. ratio

8. The number of standard deviations that a value (X) is above or below the mean is the _________________.
A. absolute deviation B. coefficient of variation C. interquartile range D. Z score

9. If the median of a distribution is greater than mean, then the distribution is _________.
A. not skewed B. symmetrical about its mean C. skewed to the left D. skewed to the
right

10. The interquartile range is _____________.

A. the largest value minus the least value B. the ratio of the mean to the standard deviation
D. Q3 - Q1 C. negative if the distribution is skewed to the left

CHAPTER TWO
Charts and Graphs

1. The width of a class interval in a frequency distribution will be approximately equal to the range
divided by _______.
A. the number of class intervals
B. the highest number in the data set
C. the lowest number in the data set
D. the midpoint of the middle class

2. If the individual class frequency is divided by the total frequency, the result is the _______.
A. midpoint frequency
B. cumulative frequency
C. stem and leaf plot
D. relative frequency

3. A cumulative frequency polygon is also called _______.

A. an ogive B. a histogram C. a frequency polygon D. a stem and leaf plot

4. A histogram can be described as _______.

A. a graphical depiction of an ogive B. a vertical bar chart
C. a vertical stem and leaf plot D. a three dimensional pie chart

5. Which of the following is best to show the percentage of a total budget that is spent on each category
of items?
A. histogram B. ogive C. stem and leaf chart D. pie chart
 Chapter 12: Analysis of Categorial Data 11

6. A cumulative frequency distribution would provide _______.

A. a graph of a frequency distribution
B. a running total of the frequencies in the classes
C. the proportion of the total frequencies which fall into each class
D. a very cloudy picture of the frequencies

7. What is the midpoint of the class interval 6 - under 9?

A. 15 B. 7.5 C. 3 D. 1.5

8. Cumulative frequencies are usually represented graphically by _______.

A. histograms B. pie charts C. ogives D. frequency polygons

9. The difference between the highest number and the lowest number in a set of data is called the _______.
A. difference B. range C. polygonal frequency D. relative frequency

10. In a histogram, the highest bar represents the class with _______.
A. the highest frequency B. the lowest frequency
C. the highest cumulative frequency D. the lowest relative frequency