Privitera Statistics Exam 1
A population can be ____ group of interest to a researcher.
any
The degrees of freedom for the sample variance
are equal to the sample size minus one
What terms refer to each of the following measures, respectively: mean, median, and mode
average, middle, and most
A researcher asks participants to estimate the height (in inches) of a statue that was in a waiting area. The researcher records the following estimates: 40, 46, 30, 50, and 34. If the researcher removes the estimate of 40 (say, due to an experimenter error), then the value of the mean will
remain the same
If a portion of people from a population are asked to complete an assessment, then the average score among that group of people would be considered a
sample mean
Which of the following values is NOT needed to compute sample variance using the computational formula, but is needed to compute the definitional formula?
sample mean
Which type of mean is used to describe a portion of individuals in a given population?
sample mean
Grouped data can be distributed
All of the above
Which of the following is consistent with the empirical rule?
all of the above
A percentile is also called a:
percentile point
The sum of relative frequencies for each interval is _____.
1.00
A relative frequency distribution is appropriate when
there are large frequency counts in each interval
A(n) ________ is a sample statistic that equals a population parameter on average.
unbiased estimator
The following frequency distribution is an example of
ungrouped data
When cumulating frequencies from the top down, the data are discussed in terms of
all of the above
Which of the following describes the definitional formula for variance?
all of the above
Which of the following is a type of graphical display used to summarize quantitative, continuous data?
all of the above
Which of the following is true about the computational formula for variance?
all of the above
Each of the following are interval scale measurements, except
marital satisfaction ratings on a 5-point rating scale
A researcher records the time (in seconds) that participants arrive late for a scheduled research study. Assuming these data are normally distributed, which measure of central tendency is most appropriate to describe these data?
mean
The ________ is the sum of all scores (in a sample or population) divided by the number of scores summed.
mean
A researcher asks adult participants to rank their top five favorite songs from their childhood. Based on the scale of measurement described, which measure of central tendency is most appropriate to describe these data?
median
The ________ is the middle value in a distribution of scores that are listed in numeric order.
median
The sum of the squared differences of scores from their mean is
minimal
To construct a pie chart, first distribute the data as
relative percentages
A characteristic (usually numeric) that describes a sample is called a
sample statistic
A researcher records the time it takes to complete a memory task in a sample of 25 participants. He finds that the average participant completed the test in 43 seconds. The average time to complete this task is called a(n)
sample statistic
Researchers measure data in a ________ to learn more about individuals in the larger _______ of interest.
sample; population
________ refer(s) to how the properties of numbers can change with different uses.
scales of measurement
Which of the following distributions has the largest variability?
scores: 1, 3, 6, 9, and 12
Which of the following is an example of a distribution with NO variability?
scores: 5, 5, 5, 5, 5, and 5
Which of the following describes a descriptive statistic?
summarize
Which of the following can be used to estimate the median?
the 50th percentile of a cumulative percentage distribution
A researcher records 17 scores. What is the median position of these scores?
the 9th score in numeric order
A researcher records the number of individual instruments identified by students listening to a piece of classical music. He splits the data into quartiles and reports that students correctly identified 3 instruments at the 25th percentile, 5 instruments at the 50th percentile, and 8 instruments at the 75th percentile. What are the IQR and SIQR for these data?
the IQR is 5; the SIQR is 2.5
A researcher records 52 scores. What is the median position of these scores?
the average of the 26th and 27th scores in numeric order
Bar charts are a lot like histograms, except
the bars displayed in the graph do not touch
How is the sample variance computed differently from the population variance?
the calculation in the denominator is different
Which of the following best describes an independent variable?
the manipulated variable
The fact that the sum of the differences of scores from their mean is zero best illustrates that
the mean is the "balance point" of a distribution
Which of the following best describes a dependent variable?
the measured behavior
You are interested in measuring the construct, work expertise. Which of the following measures for this construct is quantitative and discrete?
the number of employees that work under an employee
What is the corresponding percentile of a percentile point
the percentile rank
Which of the following measures of attraction is an example of a ratio scale measurement?
the physical proximity (in feet and inches) between two romantic partners
You are interested in measuring the construct, reinforcement. Which of the following measures for this construct is quantitative and continuous?
the size of a reward in grams
The mode is an appropriate measure of central tendency for
all of the above
The range, a measure of variability,
all of the above
The sample variance is:
all of the above
The sum of the squared deviations of scores from their mean
all of the above
Measures of variability can range in value from
0 to + ∞
A researcher records the following scores for an Olympic gymnast following her routine: 9.9, 9.8, 9.6, 9.5, 9.7, 9.1, 8.9, and 9.8. What is the range for the scores?
1.0 (9.9 to 8.9)
A researcher decides to split scores on an exam into quartiles. She determines that a score of 64 is at the 25th percentile, a score of 74 is at the 50th percentile, and a score of 80 is at the 75th percentile. What is the interquartile range (IQR) for these data?
16
A researcher computes the computational formula for SS, as finds that ∑x = 39 and ∑x2 = 271. If this is a sample of 6 scores, then what would SS equal using the definitional formula?
17.5
A researcher finds that 12% of participants make between 3-5 visits to a physician each year. What are the real limits for this interval?
2.5-5.5
A researcher reports that 12 persons in a sample of 60 reported getting between 4 and 6 hours of sleep per night. What is the relative percentage for this interval?
20%
The following is a simple frequency distribution table. If we convert this frequency distribution to relative percentages, which of the following gives the corresponding percentages in each interval listed from the top down.
20%, 13%, 17%, 33%, 17%
A researcher selects a sample of 6 males and 11 females. She asks participants to rate the likelihood they would do female-stereotyped jobs (such as nursing or school teaching) on a scale from 1 = not likely at all to 5 = very likely. Men indicated that they would be less likely to do these jobs (M = 2.1) compared with women (M = 4.3). What is the weighted mean for this entire sample of 17 participants?
3.5
What is the percentile point at the 50th percentile for the following distribution?
30
A researcher computes the definitional formula for SS, as finds that ∑(x-M)2 = 44. If this is a sample of 12 scores, then what would the value of sample variance be using the computational formula?
4.0
A researcher computes the computational formula for SS, as finds that ∑x = 22 and ∑x2 = 126. If this is a sample of 4 scores, then what would SS equal using the definitional formula?
5
As a general rule, a simple frequency distribution should have between
5 and 20 intervals
A researcher computes the definitional formula for SS, as finds that ∑(x-M)2 = 112. If this is a sample of 20 scores, then what would the value of population variance be using the computational formula?
5.6
A researcher records the following scores: 5, 3, 7, 6, 2, 8, 0, and 1. In terms of these data, the sum of the squared differences of scores from their mean is
60
A researcher records the time in seconds it takes a sample of participants to walk alone through a dark portion of campus. The researcher computes SS = 1,200. Assuming that a sample of 25 participants was observed in this study, what is the standard deviation for these data?
7.1 seconds
A psychologist treats 16 patients and records the number of sessions required to complete a behavioral therapy treatment for each patient. She computes SS = 800. Assuming the 16 patients constitute all patients under her care (so the population of her patients), what is the standard deviation for these data?
7.1 sessions
What is the percentile point at the 80th percentile in the following distribution?
8
What is the percentile point at the 90th percentile in the following distribution?
9.5
A researcher measures the time (in seconds) it takes a sample of 26 participants to respond to a stimulus presented on a computer screen. The standard deviation for response times is 6. In this example, what is the value for SS?
900
A researcher records the sound (in decibels) during a series of lessons taught by a substitute teacher at a local elementary school. In his study, he found that the sound was 80±6 (M±SD) decibels. Assuming the data are normally distributed, which of the following is an appropriate conclusion?
95% of classes were between 68 and 92 decibels.
Fill in the missing values for A and B in this frequency distribution table:
A = 3.2, B = 13
A staff member records the number of victories (per 10-game season) for a new football coach during his first three seasons with a team. The coach won 1, 3, and 8 games respectively over the three seasons. Which conclusion is appropriate?
All of the above
A researcher reports that the time (in minutes) it takes children who are "picky eaters" to finish their vegetables is negatively skewed, with children finishing their vegetables in 4.2±1.0 (M±SD) minutes. Based on Chebyshev's theorem, we can conclude that
At least 89% of children finished their vegetables in 1.2 to 7.2 minutes.
State the type of graphical display for Graph A and Graph B.
B is a bar chart; A is a histogram.
A researcher records the following motor assessment scores for two samples of athletes. Which sample has the largest standard deviation? Sample A: 8, 10, 12, 15, and 18 Sample B: 16, 18, 20, 23, and 26
Both samples have the same standard deviation.
A researcher records the following scores on a working memory quiz for two samples. Which sample has the largest standard deviation? Sample A: 2, 3, 4, 5, 6, 7, and 8 Sample B: 4, 5, 6, 7, 8, 9, and 10
Both samples have the same standard deviation.
Which of the following is NOT a characteristic of the mean?
Delete a score above the mean and the mean will increase.
A researcher measures the mean time (in seconds) it takes two groups of children to complete an activity task. She finds that Group A (M = 22 seconds) completed the task more quickly than Group B (M = 36 seconds). She then computes a weighted mean for both groups combined and calculates = 26. Based on the information provided, which group had a larger sample size?
Group A
A researcher records the following data: 4, 4, 4, 4, and 3. How would you describe the variability of the data?
It is very small (close to 0) because scores are approximately the same.
A researcher measures the amount of coffee consumed by college students while studying during the final exam week. In her study, she found that students drink 2.3±0.8 (M±SD) cups of coffee per study session. Assuming the data are normally distributed, which of the following is the most appropriate conclusion?
Most students drink between 1.5 and 3.1 cups of coffee per study session.
Which of the following is a property of the standard deviation?
Multiplying each score times the same constant will change the standard deviation by that constant.
The size of a population is symbolized as ________, whereas the size of a sample is symbolized as ________.
N; n
A researcher records the following data for the number of complaints filed (per day) following a controversial policy change at a local business: 3, 8, 5, 0, 4, 6, 2, 1, 1, 4, 2, and 0. Is the mean equal to the median in this example?
No; the mean is larger than the median.
A researcher records the following data for the number of times an interviewer is interrupted during a series of interviews: 0, 0, 3, 2, 5, 3, 0, 8, 0, 2, 1, and 1. Is the mode equal to the median in this example?
No; the median is larger than the mode.
A researcher records the following data for the time (in seconds) it takes five rats to cross an electrical grid to obtain reinforcement on the other side: 12, 9, 13, 4, and 12. Is the mean equal to the mode in this example?
No; the mode is larger than the mean.
To measure attraction, a researcher records the following data for the distance (in inches) between two persons sitting in a waiting room: 46, 32, 10, 23, 18, 46, and 60. Is the mode equal to the median in this example?
No; the mode is larger than the median.
A researcher distributes frequencies into the following intervals: 1-10, 11-20, 21-30, 31-40, 41-50, and 51 and above. What is wrong with this frequency distribution?
One interval is an open class.
Researcher A measures academic preparedness as the percent correct responses on an entrance exam; Researcher B measures academic preparedness as the current class rank of students. Which researcher measured academic preparedness as discrete data?
Researcher B
A researcher measures the number of trials it takes two samples of participants to master a new task. In both samples, SS = 240. Sample A consisted of 12 participants and Sample B consisted of 18 participants. Which sample is associated with the largest variance?
Sample A
A researcher records the number of classroom interruptions during each of two class sessions. Which session has the largest standard deviation? Session A: 12, 15, 18, 24, and 30 Session B: 8, 10, 12, 16, and 20
Sample A
A researcher records the following scores for attention during a video game task for two samples. Which sample has the largest standard deviation?
Sample B
State the problem with this simple frequency distribution.
The class intervals overlap.
When cumulating frequencies from the bottom up, the data are discussed in terms of
all of the above
A researcher distributes frequencies into the following intervals: 3-6, 7-10, 11-15, 16-18, 19-22, and 23-26. What is wrong with this frequency distribution?
The interval width is unequal.
Which of the following is NOT a rule for constructing a simple frequency distribution?
The number of intervals should equal the number of values measured.
A researcher reports that "the average shopper in the sample (n = 12) purchased $65.00 worth of items ( μ = $65.00) during a busy shopping day." What mistake was made is this citation?
The sample mean is written using the wrong notation
All other things being equal, how will the value of the sample variance be different from the population variance?
The sample variance will always be a larger value than the population variance.
Which of the following is the best explanation for why the standard deviation is almost always reported with the mean?
The standard deviation measures the spread of scores from the mean, so it is important to know both the mean and the standard deviation.
A professor grades 120 research papers and reports that the average score was an 80%. What do we know about the sum of the differences of these 120 scores from their mean of 80%?
The sum of the differences is equal to zero.
Which of the following statements about a weighted mean is true.
The weighted mean is used to compute the combined mean for two or more samples of scores in which the number of scores in each sample is disproportionate or unequal.
Researchers rarely have access to entire populations. How do researchers resolve this limitation?
They record data from a sample of people in the larger population in order to make inferences concerning characteristics in that larger population.
A researcher records the following data for the number of different food items chosen by seven participants in a buffet-style setting: 1, 6, 2, 5, 4, 3, and 7. Is the mean equal to the median in this example?
Yes
A researcher records the following data for the number of dreams recalled during a night of sleep for 10 college students: 3, 2, 4, 4, 3, 1, 1, 0, 2, and 0. Is the mean equal to the median in this example?
Yes
A researcher selects a sample of 6 professors, 6 students, and 6 administrators at a local school and has them rate the effectiveness of an innovative new teaching style. In this example, is it possible that the weighted mean ratings will equal the arithmetic mean for the entire sample of 18 participants?
Yes, because the sample sizes are equal in this example.
A researcher records the following data for how participants rated the likability (on a scale from 1 = not liked at all to 7 = very likable) of an individual who blushed after making a mistake: 5, 4, 7, 6, 6, 4, 6, 7, 2, 5, and 6. Is the mode equal to the median in this example?
Yes.
A researcher wants to determine how many participants will take less than 24 seconds to complete a cognitive performance task. If he constructs a frequency distribution for these data, what type of distribution would be most appropriate to answer his question?
a cumulative frequency distribution from the bottom up
A psychologist wants to know how many of her clients continue with therapy for at least 12 days. If she constructs a frequency distribution for these data, what type of distribution would be most appropriate to answer her question?
a cumulative frequency distribution from the top down
The SIQR can be defined as
a measure of half the distance between Q3 and Q1
A percentile is
a percentile point
Suppose that a researcher is interested in a group of 10 million people who paid to see a movie playing in theaters. In this example, the 10 million moviegoers would be regarded as
a population of moviegoers who paid to see the movie in a theater
The median is an appropriate measure of central tendency for
all of the above
Which of the following will decrease the value of the mean?
adding a score below the mean
A reason for squaring deviations to compute SS in the numerator includes which of the following?
all of the above
A researcher distributes frequencies into the following classes: absent, tardy, present. What type of data are distributed?
all of the above
A simple frequency distribution
all of the above
Descriptive statistics are procedures used to
all of the above
The mean is an appropriate measure of central tendency for
all of the above
A researcher records the number of children at a local school from single-, divorced-, and married-parent homes. This frequency data would be best displayed as a
bar chart
The mathematical term ∑x is the numerator for
both A and B
Which of the following is a type of graphical display used to summarize qualitative, discrete data?
both A and B
The following is a simple frequency distribution table. Suppose we convert this table to a cumulative frequency distribution. The frequencies in each interval of the cumulative frequency distribution would be
both A and B, depending on how the data were summarized
A researcher reports, "the average patron (n = 22) in a local bar consumed more than twice the number of drinks (per day) on weekends (M = 5.4 drinks) compared to weekdays (M = 2.3 drinks)." Although not stated directly, how do we know that the patrons in this study constitute a sample, and not a population of patrons at this local bar?
both B and C
Quantitative measures can be
both a and b
Ungrouped data can be distributed as
categories
Adding the same constant to each score in a distribution (or subtracting the same constant from it) will
cause the mean to change by that constant
Multiplying or dividing each score in a distribution by the same constant will
cause the mean to change by that constant
Qualitative data varies by ________; quantitative data varies by ________.
class; amount
The procedure of converting a categorical variable to numeric values, is called:
coding
________ are measured along a continuum at any place beyond the decimal point.
continuous data
Based on the following graphical summary display, what research design was used to record and analyze these data?
correlational
________ is the variable that is believed to change in the presence of the independent variable.
dependent variable
A researcher records the number of votes for each of five candidates running for class president. Based on her presentation of the following results, what type of statistics did she use?
descriptive statistics
The use of tables and graphs to summarize data is an example of
descriptive statistics
A researcher selects a sample of 24 participants and has them complete a survey on dating preferences. In this example, what are the degrees of freedom for sample variance and what does this figure represent?
df = 23; it represents the number of scores that are free to vary in a sample.
The sample variance is computed by dividing SS by ____; whereas the population variance is computed by dividing SS by ____.
df; N
A health practitioner measures the heart rate (in beats per minute) of patients under low, moderate, and high-stress levels. Heart rate can be best described as
discrete data
________ are measured in whole units or categories that are not distributed along a continuum.
discrete data
Recording the number of dreams recalled is an example of ________ data; whereas recording the time (in minutes) spent in a dream stage of sleep is an example of ________ data.
discrete; continuous
The mean would be used to describe which of the following variables?
distance traveled in miles
Why is it important to divide by df to compute sample variance?
doing so makes the sample variance an unbiased estimator of the population variance
The definitional formula ______ the computational formula for SS.
equals
Statistical analysis allows researchers to
evaluate scientific observations
A researcher tests whether the dosage level of some drug (low, high) causes significant differences in health. To do this, the researcher randomly assigns rat subjects to receive a low or high dosage of the drug and records health-related measures in both groups. The type of method described is
experimental
Which of the following research designs is used to determine the causes of behavior that help to explain why the behavior occurs?
experimental
Three research methods common to research in the behavioral sciences are
experimental, quasi-experimental, and correlational
The three steps for constructing a simple frequency distribution are
find the real range, find the interval width, and construct the frequency distribution
A therapist observes that spouses are more likely to forgive their partners for lying to them if they find out the truth from their spouse and not a third party. In this example, the dependent variable is
forgiveness
Which of the following requires the calculation of a real range?
frequency distributions for grouped data
A ________ is plotted at the midpoint of each interval, whereas a ________ is plotted at the upper boundary of each interval.
frequency polygon; ogive
A researcher summarizes a set of frequency data into five intervals. This is an example of a frequency distribution for
grouped data
Interval scales of measurement
have equidistant scales
A graphical display for grouped frequency distributions with continuous data is called a
histogram
A researcher measures the time (in seconds) that it takes children to complete a basic reading skills task. What type of graphical display would be most appropriate for summarizing the frequency of children falling into different intervals of time?
histogram
A researcher measures the weight (in ounces) of newborn infants in the month of March. What type of graphical display would be most appropriate for summarizing the frequency of infants falling into different intervals of weight?
histogram
A researcher asks participants to estimate the calories they consume in a meal. The researcher records the following estimates: 450, 426, 310, 500, and 220. If the researcher removes the estimate of 220 (perhaps because the participant drops out of the study), then the value of the mean will
increase
________ is the variable in an experiment that is manipulated between conditions being observed.
independent variable
Procedures that allow researchers to infer or generalize observations made with samples to the larger population from which they were selected best describes
inferential statistics
The range of scores between the upper and lower quartiles of a distribution is called the
interquartile range
A researcher measures the body temperature (in degrees Fahrenheit) of participants immediately before and immediately following sleep. Temperature is on what scale of measurement?
interval
The range of scores in each interval of a grouped frequency distribution is called the
interval width
Grouped data are distributed into ________, whereas ungrouped data are distributed into ________.
intervals; categories
The advantage of squaring the deviation of each score from the mean and then summing is that
it produces a minimal positive solution that is not zero, so long as all scores are not exactly the same value
The distribution of personal income for U.S. citizens is positively skewed. If the median annual income is $44,000, this implies that the mean annual income is
larger
A researcher records the hospital admission rates for coronary heart disease at 10 local hospitals. She finds that 2 different hospitals had the highest overall rates of hospital admissions. Which measure of central tendency did this researcher use to describe these data?
mode
The ________ is the value that occurs most often or at the highest frequency in a distribution.
mode
The variance and standard deviation can never be
negative
A researcher records a sample of 30 exam scores and finds that the population variance for these data is larger than the sample variance. Is this possible?
no, the sample variance will be larger because SS is divided by degrees of freedom in the denominator of the variance formula
An animal researcher measures the number of times a rat presses a lever located at the right, center, and left of a cage for a food reward. What scale of measurement is the location of lever pressing?
nominal
An education counselor records the number of high school graduates enrolled in community colleges, four-year colleges, and universities. What scale of measurement is the type of college?
nominal
State the four scales of measurement in order from least informative to most informative.
nominal, ordinal, interval, ratio
Which of the following terms are least likely to be used to describe qualitative data?
numeric
Which graphical display lists percentages and not original scores
ogive
A consultant ranks the five most needed areas of improvement for a local business. What scale of measurement are the rankings?
ordinal
A movie critic rates a movie on a scale from one (lowest) to four (highest) stars. What scale of measurement are the ratings?
ordinal
A cumulative percentage summary that indicates the percentage of scores at or below a given value is called a
percentile rank
The ________ is the percentage of scores with values that fall below a specified score in a distribution, is called the:
percentile rank
Each of the following is an example of quantitative data, except
political affiliation
A characteristic (usually numeric) that describes a population is called a
population parameter
A psychologist reviews her notes for all her patients and determines that on average her patients complete therapy in 24 days. The average time to complete therapy among all her patients is called a(n)
population parameter
Recording whom students study with describes ________ types of data; whereas recording the number of hours spent studying per week describes ________ types of data.
qualitative; quantitative
Grouped data are to ungrouped data as
quantitative is to qualitative
________ data describe numeric aspects of phenomena; whereas ________ data describe nonnumeric aspects of data.
quantitative; qualitative
Three key elements of control that allow researchers to draw cause-and-effect conclusions are
randomization, manipulation, and comparison/control
The median would be used to describe which of the following variables?
rankings
A researcher compares the amount of college debt (in dollars) that undergraduate students incur up to their four-year degree. College debt is on what scale of measurement?
ratio
To determine the interval width, we divide the ________ by the number of intervals.
real range
A researcher identifies college students as a group of interest to test her hypothesis. She then identifies a few local college students and selects a small group of the local college students to be observed. In this example, the sample is:
the small group of college students who here observed
A student scores in the 80th percentile on an exam. What does this mean in comparison to all other students?
the student scored higher than 80% of all others who took the exam
An interquartile range removes
the top and bottom 25% of scores in a distribution before calculating range
A percentile point is
the value of a score on a measurement scale below which a specified percentage of scores in a distribution fall
All other things being equal (so assuming that the value of SS never changes), as sample size increases,
the value of sample variance decreases
Which characteristic of a histogram implies that it summaries continuous data?
the vertical bars touch at the upper boundary of each interval
A measure of the average squared distance of scores from the mean is called the
variance
The mode can be used with the mean to describe which of the following variables?
volume in a container
The ________ is an arithmetic mean of a weighted or disproportionate set of scores.
weighted mean
When would a researcher calculate a population mean?
when data are measured for all members of a population
Each deviation in the numerator for variance is squared because
without squaring each deviation, the solution for SS would be zero
Given the same set of data for a population and sample, would the mean for both data sets be equal?
yes, this would be true anytime both data sets are the same
Which of the following is not a symbol used with samples:
μ
The population mean is symbolized as ________, whereas the sample mean is symbolized as ________.
μ; M