Stats Exam 1
Which of the following z-scores represents the location closest to the mean?
+1.25 -0.25* -2.50 +0.75
If a population with μ = 122.51 and σ = 17.45 is transformed into z-scores, then the resulting distribution of z-scores will have a mean of _____ and a standard deviation of _____.
122.51; 17.45 122.51; 1 0; 1* 0; 17.45
What position in the distribution corresponds to a z-score of z = -1.50?
Below the mean by a distance equal to 1.50 standard deviations* Below the mean by 1.50 points Above the mean by 1.50 points Above the mean by a distance equal to 1.50 standard deviations
When analyzing a variable measured on an interval scale, which measure of central tendency would be most appropriate to report (assuming the distribution is normal)?
Mean* Median Statistic Mode
The mean for any distribution corresponds to a z-score of ____
N 1 Cannot be determined from the information given. 0*
Which of these is based on all of the scores in a set of data?
Range Mode Variance* Median
A grouped frequency distribution table lists one interval as 20-29. The width of this interval is 9 points
True False*
Every dataset will have a mode
True False*
The relationship between a statistic and a parameter is the same as the relationship between _____
a statistic and a sample descriptive statistics and inferential statistics a parameter and a population a sample and a population*
If a variable can be divided into an infinite number of fractional parts, then it is a(n) _____ variable
continuous* discrete independent dependent
For a particular sample size of n = 15, the largest distance (deviation) between a score and the mean is 9 points. The smallest distance between a score and the mean is 5 points. Therefore, the standard deviation will be ____
equal to 0 less than 5 between 5 and 9* greater than 9
You would use a _____ to illustrate data for a variable measured at the _____ scale of measurement.
frequency polygon; nominal histogram; ordinal bar chart; nominal* pie chart; interval
Using letter grades (A, B, C, D, and F) to classify student performance on an exam is an example of measurement on a(n) _____ scale of measurement.
interval nominal interval ordinal*
One relative strength of the _____ as a measure of central tendency is that it ____
mean; is based on all of the scores in a distribution* mean; is not influenced by outliers median; describes bimodal distributions mode; describes skewed distributions
The _____ may be defined as _____
mean; the most common or frequently occurring score in a distribution median; the mathematical average mean; the mathematical average* mode; the score that splits a distribution into two equal halves
Calculating the variance involves _____ deviations because ____
subtracting; deviations are always positive multiplying; samples are smaller than populations squaring; the sum of unsquared deviations is equal to 0* dividing; distributions are sometimes skewed or asymmetric
The normal distribution is _____
symmetric* negatively skewed positively skewed asymmetric
You would use a _____ to illustrate data for the variable "Cost of a new vehicle.
Frequency distribution table Bar chart Normal distribution Histogram*
Which of the following can be a negative number?
The sum of squared deviations (SS) The mean (μ and M)* The standard deviation (σ and s) The variance (σ² and s²)
Which of the following is a reason why researchers examine data by creating tables and figures?
To calculate inferential statistics To gain an initial understanding of their data To identify their independent and dependent variables To prove their research hypothesis*
Which of the following is a reason why researchers examine data by creating tables and figures?
To determine their research hypothesis To figure out which variable is the independent variable To understand the shape of the distribution* To define their population of interest
The mean is considered to be the "balance point" for a distribution because exactly half of the scores are located above the mean and exactly half are below the mean.
True False*
The scores for a very easy exam would probably form a positively skewed distribution.
True False*
A correlational study is used to examine the relationship between two variables but cannot determine whether it is a cause-and-effect relationship.
True* False
A grouped frequency distribution table does not provide enough information to obtain a complete listing of the original set of scores.
True* False
A histogram is constructed so that adjacent bars touch.
True* False
A raw score with a value less than or equal to the mean will have a z-score that is less than or equal to 0.
True* False
One relative weakness of the _____ as a measure of central tendency is that it ___
median; is influenced by outliers mean; does not take into account all of the scores mode; is influenced by outliers mean; is influenced by outliers*
One relative weakness of the _____ as a measure of central tendency is that it ____
mode; is influenced by outliers median; doesn't describe bimodal distributions* mean; isn't based on all of the scores in the distribution median; is influenced by outliers
A researcher uses an anonymous survey to investigate the study habits of American college students. Based on the set of 92 surveys that were completed and returned, the researcher finds that these students spend an average of 4.7 hours each week working on course material outside of class. For this study, the average of 4.7 hours is an example of a _____
sample statistic* population parameter
The smallest score in a population is X = 5 and the largest score is X = 10. Based on this information, you can conclude that the ____
standard deviation is greater than 8 mean is greater than 10 mean is equal to 0 standard deviation is smaller than 5*
The mode may be defined as
the mathematical average. the difference between the lowest and highest score in a data set. the most common or frequently occurring score in a distribution.* the average squared deviation of a score from the mean.
The range is defined as
the mathematical difference between the lowest and highest scores in a data set.* average squared deviation of a score from the population mean. the middle 50% of the scores in a set of data. average squared deviation from the mean.
The median may be defined as
the most common or frequently occurring score in a distribution. the average squared deviation of a score from the mean. the difference between the lowest and highest score in a data set. the score that splits a distribution into two equal halves.*
Variance may be defined as
the score that splits a distribution into two equal halves. the most common or frequently occurring score in a distribution. the average squared deviation of a score from the mean.* the mathematical average.
In an experiment comparing two methods for teaching social skills training to children with autism, the independent variable is _____ and the dependent variable is _____
the social skills that are learned; the children receiving the training teaching methods; the social skills that are learned* teaching methods; the children receiving the training the children receiving the training; the social skills that are learned
Which of these is based on all of the scores in a set of data?
The range The median The mode The mean*
Of the following z-score values, which one represents the most extreme location on the left-hand side of the distribution?
+2.00 +1.00 -2.00* -1.00
For a population with σ = 10, a score that is located 20 points above the mean would have a z-score of _____.
+2.00* -2.00 +20.00 Cannot be determined without knowing the value of the mean
Which of the following is an advantage of transforming raw scores into z-scores?
All scores are moved closer to the mean. All negative numbers are eliminated. None of these options are an advantage.* The distribution is transformed into a normal shape.
In a research study comparing characteristics of left-handed and right-handed individuals, handedness (left-handed or right-handed) is an example of what kind of variable?
An independent variable A quasi-dependent variable A dependent variable A quasi-independent variable*
Which of the following is true for most distributions?
Around 50% of the scores will be located within one standard deviation of the mean. Around 90% of the scores will be located within one standard deviation of the mean. Around 70% of the scores will be located within one standard deviation of the mean.* Around 30% of the scores will be located within one standard deviation of the mean
For which of these variables would you create a grouped frequency distribution table to summarize the data you've collected?
College major (Math, Nursing, English, etc.) Type of housing (Dorm, Apartment, House) Distance from campus (Miles)* Year in school (Freshman, Sophomore, Junior, Senior)
Which of the following is a strength of the range?
It accurately reflects the amount of variability in the entire distribution of scores It can be used in statistical analyses designed to test research hypotheses It represents the variability in a set of data while lessening the influence of outliers It provides information about the sample from which the data were collected*
All of the following are strengths of the mode EXCEPT which of the following?
It is an actual score for the variable. It describes a bimodal or multimodal distribution. It is used to test a hypothesis.* There are no calculations to find the mode.
Which of the following is a weakness of the range?
It is difficult to compute It lessens the influence of outliers by only taking into consideration 50% of the distribution It may not accurately reflect the amount of variability in the entire distribution* It takes into account all the scores of a distribution
One the first day of classes, students are asked to list their major (Chemistry, Exercise Science, Theology, etc.). What type of frequency distribution graph would be best to display their responses to this question?
Normal distribution Frequency polygon Bar chart* Histogram
What frequency distribution graph is appropriate for scores measured on a nominal scale?
Only a polygon Only a histogram Only a bar graph* Either a histogram or a polygon
The students in a psychology class seemed to think that the midterm exam was very easy. If they are correct, what is the most likely shape for the distribution of exam scores?
Positively skewed Negatively skewed* Normal Symmetrical
Which of these is based on all of the scores in a set of data?
Range Median Mode Standard deviation*
When analyzing a variable with four unranked categories, which measure of central tendency would be most appropriate to use?
Sample Median Mean Mode*
Which of these is influenced by outliers?
The mean* The median The mode All of the above
You have a dataset with 100 observations. You randomly select one value in the dataset and add 5 points to it. Which of the following is the most likely to change?
The median will change The mode will change The mean, median, and mode all have the same likelihood of changing The mean will change*
Which of the following is NOT a guideline for creating grouped frequency distribution tables?
The number of intervals should accurately represent the data. Intervals should not overlap. Intervals should be of equal size. The data are grouped into arbitrary intervals.*
A population with µ = 30, a score of X = 24 corresponds to z = -2.00. The standard deviation for the population is σ = 6.
True False*
A recent report concluded that children with siblings have better social skills than children who grow up as an only child. This is an example of an experimental study.
True False*
Adding a new score to a distribution will always change the value of the mean.
True False*
After a researcher adds 5 points to every score in a sample, the standard deviation is found to be s = 10. The original sample had a standard deviation of s = 5.
True False*
Any individual with a negative z-score has a raw score greater than the mean.
True False*
Constructs are external attributes or characteristics that can be directly observed to describe and explain behavior.
True False*
For a negatively skewed distribution, the mean usually has a larger value than either the median or the mode.
True False*
If a set of scores covers a range of 80 points, the grouped frequency distribution table should use an interval width of 8 points.
True False*
If it is appropriate to present a distribution of scores in a polygon, then it would also be appropriate to present the scores in a bar graph.
True False*
If you have a score of X = 76 on an exam with µ = 70, you should expect a better grade if σ = 10 than if σ = 5
True False*
In February in South Dakota, the daily high temperatures are typically low with only a few relatively warm days. A frequency distribution graph showing the daily high temperatures would probably form a negatively skewed distribution.
True False*
In a distribution with s = 20, a score that is above the mean by 10 points will have a z-score of z = -0.50.
True False*
In a grouped frequency distribution table, the top value in each class interval should be a multiple of the interval width.
True False*
In a population with a mean of µ = 40 and a standard deviation of σ = 8, a score of X = 46 would be an extreme value, far out in the tail of the distribution.
True False*
In an experimental study, individuals in a control condition receive the experimental treatment.
True False*
Multiplying every score in a sample by 3 will not change the value of the standard deviation.
True False*
To determine how much difference there is between two individuals, you must use either a nominal or an ordinal scale of measurement
True False*
If a set of exam scores form a negatively skewed distribution, it suggests that the majority of the students did not score well on the exam.
True False*
It is possible to have a distribution of scores where no individual has a score exactly equal to the mode.
True False*
A recent report concluded that college graduates have higher life-satisfaction scores than individuals who do not receive college degrees. For this study, graduating versus not graduating is an example of a quasi-independent variable.
True* False
After a researcher multiplies every score in a sample by 2, the standard deviation is found to be s = 10. The original sample had a standard deviation of s = 5.
True* False
An operational definition identifies a set of operations for measuring an external behavior and then uses the resulting measurement as a definition of a hypothetical construct.
True* False
Because all z-score distributions have the same mean and standard deviation, the z-score distribution is called a standardized distribution.
True* False
Changing the value of a score in a distribution will always change the value of the mean.
True* False
For a distribution with one or two extreme scores, the median is usually a more representative value than the mean.
True* False
For a population with a mean of µ = 72, any score greater than 72 will have a positive z-score.
True* False
For a population, a deviation score is computed as X - µ.
True* False
For a sample with M = 20 and s = 1, a score of X = 17 would be considered an extremely low score.
True* False
For any distribution of scores, the location identified by z = +1.00 and the location identified by z = -1.00 are exactly the same distance from the mean.
True* False
For severely skewed distributions, the median often provides a better measure of central tendency than the mean.
True* False
For statistical purposes, there usually is not much difference between scores from an interval scale and scores from a ratio scale.
True* False
If a sample has an odd number of scores, at least one individual will have a score exactly equal to the median.
True* False
If two individuals in the same population have identical X values, they also will have identical z-scores.
True* False
In a grouped frequency distribution table, one interval is identified as 30-34. This interval has a width of 5 points.
True* False
It is easier to see the mean difference between two samples if the sample variances are small.
True* False
Standardized scores are "simple" values for the mean and standard deviation that do not change any individual's location within the distribution.
True* False
Students in an introductory business class are classified as either business majors and non-business majors. This is an example of a measurement on a nominal scale.
True* False
The goal of an experiment is to demonstrate that changes in one variable are responsible for causing changes in a second variable.
True* False
The process of transforming every X value in a distribution into a corresponding z-score to create a distribution of z-scores is called a z-score transformation.
True* False
The range and the standard deviation are both measures of spread.
True* False
The range is usually considered to be a relatively crude measure of variability.
True* False
There are situations for which it is either impossible to compute a mean or the mean does not provide a central representative value.
True* False
Under what circumstances is a score that is located 5 points above the mean considered a central value that is relatively close to the mean?
When the population standard deviation is much less than 5. When the population standard deviation is much greater than 5.* When the population mean is much less than 5. When the population mean is much greater than 5.
Under what circumstances is a score that is 15 points above the mean an extreme score relatively far from the mean?
When the population standard deviation is much smaller than 15* When the population mean is much larger than 15 When the population mean is much smaller than 15 When the population standard deviation is much larger than 15
Which of the following represents the deviation score?
X s² μ (X - μ)*
In a grouped frequency distribution, which of the following statements is true?
You are only interested in percentile rank and not frequency, because the individual data points are not used. You no longer know what the exact data points in the data set are.* It is only a good idea when the difference between the smallest and largest observation is greater than 100. It makes small data sets more easily read.
You would use a _____ to illustrate data for a variable measured at the _____ scale of measurement.
bar chart; ratio histogram; interval* frequency polygon; ordinal pie chart; ratio
Statistical methods that organize, summarize, or streamline data are called
descriptive statistics* sample statistics population parameters inferential statistics
The direct, unchanged scores that are the direct result of measurement are called
deviation scores. z-scores. raw scores.* standardized scores.
One relative strength of the _____ as a measure of central tendency is that it ____
median; can be used in statistics designed to test research hypotheses mean; describes bimodal distributions mode; isn't influenced by outliers* mode; is based on all of the scores in the distribution
One relative weakness of the _____ as a measure of central tendency is that it ____.
median; is influenced by outliers mean; does not take into account all of the scores mode; does not take into account all of the scores* mode; is influenced by outliers
In a distribution that is positively skewed, scores with the highest frequencies are
in the middle of the distribution. on the left side of the distribution.* represented at two distinct peaks. on the right side of the distribution.
If a variable CANNOT be divided into an infinite number of fractional parts, then it is a(n) _____ variable.
independent discrete* dependent continuous
The average math ACT score for the entire class of incoming first-year college students is 21. However, if you select a sample of 25 first-year students and compute their average math ACT score you probably will not get exactly 21. What statistical concept is used to explain the natural difference that exists between a sample mean and the corresponding population mean?
inferential error statistical error sampling error* parametric error
Grouped frequency distribution tables are created to summarize data for variables measured at the _____ level of measurement.
interval or ratio* nominal or interval ordinal or ratio nominal or ordinal
One relative strength of the _____ as a measure of central tendency is that it _____.
mean; is not influenced by outliers median; describes skewed distributions* mode; is based on all of the scores in a distribution mean; describes bimodal distributions
A z-score of z = +3.00 indicates a location that is
near the center of the distribution. the location depends on the mean and standard deviation for the distribution. far above the mean in the extreme right-hand tail of the distribution.* slightly above the mean.
State the four scales of measurement in order from least informative to most informative.
nominal, ordinal, ratio, interval nominal, ordinal, interval, ratio* ordinal, nominal, ratio, interval ordinal, nominal, interval, ratio
A researcher uses an anonymous survey to investigate the study habits of American college students. Based on the set of 92 surveys that were completed and returned, the researcher finds that these students spend an average of 4.7 hours each week working on course material outside of class. For this study, the set of 92 students who returned surveys is an example of a _____
parameter statistic population sample*
A characteristic that describes a population, usually a numerical value, is called a _____
parameter* statistic population sample
Procedures that allow researchers to infer or generalize observations made with samples to the larger population from which they were selected best describe
population statistics sample statistics inferential statistics* descriptive statistics
A researcher uses an anonymous survey to investigate the study habits of American college students. The entire group of American college students is an example of a _____.
population* parameter sample statistic
The _____ measures the _____ of a distribution of scores for a variable
range; symmetry standard deviation; variability* variance; symmetry mean; variability
Determining a person's reaction time (in milliseconds) would involve measurement on a(n) scale of measurement.
ratio* ordinal nominal interval
For a variable measured at the _____ scale of measurement, one would use a _____ to illustrate the data
ratio; bar chart interval; pie chart ratio; frequency polygon* nominal; histogram
You would calculate the population standard deviation (σ) for a collected set of data when
you have collected data from a sample. you want to test hypotheses about populations. your sample is larger than the population. you have collected data from the entire population.*
You calculate a value of -1.87 for the variance for a set of data. This necessarily implies that
you need to check your calculations.* most of the scores are less than the mean. there are outliers in the data. the distribution of scores in negatively skewed.
College GPAs can range from 0.00 to 4.00. You collect GPAs from a sample of students and calculate a standard deviation of 6.13. This most likely implies that
you need to check your calculations.* the distribution of GPAs is bimodal. the distribution of GPAs is symmetrical. there is a great deal of variability in the GPAs of your sample
You have a score of X = 65 on an exam. Which set of parameters would give you the best grade on the exam?
µ = 60 and σ = 10 µ = 70 and σ = 5 µ = 60 and σ = 5* µ = 70 and σ = 10
A very bright student is described as having an IQ that is three standard deviations above the mean. If this student's IQ is reported as a z-score, the z-score would be _____
μ + 3 μ + 3σ +3.00* Cannot be determined from the information given.
A population has µ = 50. What value of σ would make X = 55 a more central, representative score in the population?
σ = 10 σ = 5 σ = 1 σ = 20*
