Test 1
Which of the following is consistent with the empirical rule?
-68% of all scores lie within one standard deviation of the mean. -95% of all scores lie within two standard deviations of the mean. -99.7% of all scores lie within three standard deviations of the mean.
Distinguish between descriptive and inferential statistics
-Descriptive: is used to summarize, organize, and make sense of a set of scores. -Inferential: is used to allow researchers to infer or generalize observations made with samples to the larger population from which they were selected
Which of the following is true about the computational formula for variance?
-The computational formula will always produce the same solution as the definitional formula (give or take rounding errors). -It is a short-cut method for calculating variance when the population or sample size is large. -It is derived mathematically from the definitional formula.
Explain why the sample variance and population variance are computed differently.
-The sample variance is used to measure how dispersed scores are from their mean when the data consist of less than an entire population of scores. -Whereas a population variance is used to measure the dispersion of scores from their mean.
The sample variance is:
-an unbiased estimator of the population variance -associated with n - 1 degrees of freedom -computed by dividing SS by df
A simple frequency distribution
-can be used to summarize grouped data -can be used to summarize ungrouped data -summarizes the frequency of scores in a given category or range
The mode is an appropriate measure of central tendency for
-data that are bimodal -use with other measures of central tendency -data that are on a nominal scale
The mean is an appropriate measure of central tendency for
-data that are normally distributed -data that are on an interval or ratio scale -data in which the mean, median, and mode are equal
The median is an appropriate measure of central tendency for
-data that are positively skewed -data that are negatively skewed -data that are on an ordinal scale
When cumulating frequencies from the top down, the data are discussed in terms of
-greater than -at or above -at least
Which of the following is a type of graphical display used to summarize quantitative, continuous data?
-histogram -frequency polygon -ogive
A researcher distributes frequencies into the following classes: absent, tardy, present. What type of data are distributed?
-nominal data -qualitative data -ungrouped data
Descriptive statistics are procedures used to
-summarize a set of scores or observations -organize a set of scores or observations -make sense of a set of scores or observations
The mathematical term ∑x is the numerator for
-the population mean -the sample mean
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 records the time in seconds it takes a sample of participants to walk alone through a dark portion of campus. The researcher computes SS = 1,000. Assuming that a sample of 11 participants was observed in this study, what is the standard deviation for these data?
10 seconds
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 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%
Which of the following requires the calculation of a real range?
frequency distributions for grouped data
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
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
A researcher computes the definitional formula for SS, as finds that ∑(x-M) = 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 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.
What is the definition of an operational definition?
A description of some observable event in terms of specific process or manner by which it was observed or measured.
Give the definition of variance in words.
A measure of variability for the average squared distance that scores deviate from their mean.
What is the variance a preferred measure of variability?
A preferred estimate of variability is the variance because it includes all scores, not just 2 extreme scores, to estimate variability.
Why is the mean a preferred measure of central tendency?
Because it is the most commonly reported measure of central tendency
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.
________ is the variable that is believed to change in the presence of the independent variable.
Dependent variable
A researcher records the following data: 4, 4, 4, 4, and 3. How would you describe the variability of these data?
It is very small (close to 0) because scores are approximately the same.
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.
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.
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
According to the empirical rule, for data that are normally distributed, at least _____% of data lie within 2 standard deviations from the mean.
The empirical rule states that for data that are normally distributed, at least 95% of data lie within 2 standard deviations of the mean.
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.
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.
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.
Describe SS (Sum of squares) in words.
The sum of the squared deviations of scores from their mean. SS is the numerator in the variance formula.
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.
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 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
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 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
Qualitative data varies by ________; quantitative data varies by ________.
class; amount
Based on the following graphical summary display, what research design was used to record and analyze these data?
correlational
The scale of measurement a researcher uses
determines the type of inferential statistics that can be done
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.
Each of the following are interval scale measurements, except
duration of sleep (in hours)
The definitional formula ______ the computational formula for SS.
equals
Statistical analysis allows researchers to
evaluate scientific observations
Which of the following research designs is used to determine the causes of behavior that help to explain why the behavior occurs?
experimental
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
Interval scales of measurement
have equidistant scales
A graphical display for grouped frequency distributions with continuous data is called a
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
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 in each interval of a grouped frequency distribution is called the
interval width
In the stem-and-leaf display, each number to the right of the vertical line is referred to as a ________; the numbers to the left of the vertical line are called the ________.
leaf; stem
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
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
When can variability be negative?
never
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
A consultant ranks the five most needed areas of improvement for a local business. What scale of measurement are the rankings?
ordinal
The correct order of operations in math, is:
parentheses, roots, exponents, multiplication, division, addition, and subtraction
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
Three key elements of control that allow researchers to draw cause-and-effect conclusions are
randomization, manipulation, and comparison/control
To construct a pie chart, first distribute the data as
relative percentages
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____ (Hint: Calculate the mean first!)
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
A characteristic (usually numeric) that describes a sample is called a
sample statistic
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
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
Define the Median...
the middle value in a distribution of data listed in numeric order
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
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
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
Regardless of the number of scores in a distribution, the range only includes ___ score(s) in its calculation.
two
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