Chapter 3- Displaying Data
For the following set of data [5 9 5 5 2 4] the mean is
4
5
5
6
The median has at least one advantage over the mean in thaat
It is not much affected by extreme scores
It is easier to calculate than the mode
It is usually closer tio the population mean than the mode
It varies less from sample to sample
In which of the following situations would you be most likely to use the mean as a measure of central tendency?
You want to report data on family income so we know how families are doing
You want to measure something that has a number of ourliers
You want to report the average weight of airline passengers so that the pilot can estimate the weight of the plane
Your poss wants to know what size T-shirts to order for the next company picnic
Which of the following statements about the mode is false?
It must be an actual score that occurred in the data set
It can consist of more than one number
It can be calculated algebraically
All of the above are false
We are most likely to randomly pick which score from an actual data set?
The mode
The median
The highest score
The lowest score
The median location is defined as
∑X/N
(N+1)/2
p(Xi=mode) > p(Xj= any other score)
The average score
The chief disadvantage of the median, when compared to the mean, is that
It is less stable than the mean from sample to sample
Its location cannot be calculated algebraically
It is disproportionately affected by outliers
It has no disadvantages
When the distribution is symmetric, which of the following are always equal?
Mean and mode
Median and mode
Mean and median
Mean, median, and mode
X-bar is the symbol commonly used for the
Mean
Mode
Median
None of the above
The measure of central tendency that is most useful in estimating population characteristics because it is less variable from sample to sample is the
Mode
Median
Mean
All of the above are equally useful in estimating characteristics of the population
Alison received a score of 480 on the verbal portion of her SAT. If she scored at the 50th percentile, her score represents the _________ of the distribution of all verbal SAT scores.
Mean
Median
Mode
Average
On a histogram, which always refers to the highest point on the distributions?
Mean
Median
None of the above
Mode
For the data set [1, 3, 3, 5, 5, 5, 7, 7, 9], the value "5" is
The mode
The median
The mean
All of the above
For the following data set [1, 9, 9, 9, 11, 28] which of the following is false?
The mode is 9
The median is 9
The mean is 9
The median location is 3.5
Professor Neuberg found that the mean number of alcoholic drinks consumed at a part was much higher for males than for females. If the median and mode number of drinks consumed by males and females was both zero, how can the difference in means be explained?
THe mean number of drinks consumed by females was disproportionately increased by outliers drinking lots of drinks.
The mean number of drinks consumed by males was disproportionately increased by outliers drinking lots of drinks.
The difference in means gives no information that is useful and should not be explained.
The difference most likely comes from an error in calculation.
If a store manager wanted to stock the men's clothing department with shirts fitting the most men, which measure of central tendency of men's shirt sizes should be employed?
Mode
Mean
Median
Average
When we make implicit assumptions about a scale having interval properties
We are probably calculating a mode
We are probably calculating a median
We are assuming the distance between 4 and 6 is the same as the distance between 6 and 8
We are always making unreasonable assumptions
Dispersion refers to
The degree to which data cluster toward one end of the scale
The centrality of the distribution
The degress to which individual data points are distributed around the mean
All of the above
If we eliminate the top and bottom 25% of the data and take the range of what remains we have the
Range
Adjusted range
Interquartile range
Quartile variance
The population variance is
An estimate of the sample variance
Calculated exactly like the sample variance
A biased estimate
Usually an unknown that we try to estimate
When calculating the standard deviation we divide by N-1 rather than N because the result is
Smaller
Less biased
Easier to interpret
Equal to the population mean
What da statistic whose average is very stable o we mean by an unbiased statistic?
A statistic that equals the sample mean
A statistic whose average is very stable from sample to sample
A statistic used to measure racial diversity
A statistic whose long range average is equal to the parameter it estimates
The verticle line in the center of a box plot
Represents the sample mean
Represents the sample median
Serves to anchor the box
Can represent anything you want it to
The whiskers in a boxplot
Always enclose all of the data points
Always run from the smaller inner fence to the larger inner fence
Encompass the H-spread only
Contain all data points outside the box except the outliers
Data points that lie outside the whiskers in a boxplot are often referred to as
Incorrect values
Outliers
Representative values
Deviates
People in the stock market refer to a measure called the standard deviation, although it is calculated somewhat differently from the one discussed here. It is a good guess that this measure refers to
The riskiness of the stock
The value of the stock
How much the stock price is likely to fluctuate
How much money you are likely to earn from buying that stock
If we multiple a set of data by a constant, such as converting feet to inches, we will
Leave the mean and variance unaffected
Multiply the mean and the standard deviation by the constant
Multiple the mean by the constant but leave the standard deviation unchanged
Leave the mean unchanged but alter the standard deviation
The university counseling center has treated a large number of students for depression. They find that the standard deviation of depression scores for their pool of students is substantially higher after treatment than before treatment. The most likely explanation is
Some students improve more than others
Some students improved substantially while others actually got worse
Depression therapy at the counseling center affects different students differently
All of the above
If we know that a set of test scores has a mean of 75 and a standard deviation of 8, we would conclude that
The average deviation from the mean is about 8 points
The average person will have a score of 75 + 8 = 83
More people are above 75 than below it
You can't tell anything about how scores lie relative to the mean
The range is
The difference between the inner fences
The H-spread
Not influenced very much by outliers
The difference between the highest and lowest score
The problem with measuring dispersion by merely averaging all the deviations between each score and the overall mean is that
Positive and negative deviations will balance out
Squared values make intuitive interpretation difficult
Dividing by (N-1) gives a biased statistic
There are no problems with measuring dispersion this way
The equation "(median location +1)/2" is used to calculate the
Median
Hinge location
Outer fence
Inner fences
The interquartile range
Is the 50th percentile score in a data set
Contains as few as 25% of scores or as many as 75% of scores in a data set
Contains the middle 50% of scores in a data set
Is the same as the range
Errors that can lead to outliers can occur in
Measurement
Data recording
Data entry
All of the above
Given the numbers 1, 2, and 3, the standard deviation is
0
1
0.667
The square of the variance
A "hinge" is another word for
The median
A quartile
The range
Boundary
We normally compute the variance using N-1 in the denominator because
It is easier that way
It leads to an unbiased estimate of the sample variance
It leads to an unbiased estimate of the population variance
It overestimates that population variance
Data points at the extremes of the distribution have
Little effect on the variance
Distort the usefulness of the median
More effect on the variance than scores at the center of the distribution
Are undoubtedly incorrect
We care a great deal about areas under the normal distribution because
They translate directly to expected proportions
They are additive
They allow us to calculate probabilities of categories of outcomes
All of the above
The difference between the histogram of 175 behavior problem scores and a normal distribution is
The normal distribution is continuous, while behavior problems scores are discrete
The normal distribution is symmetric, while behavior problem scores may not be
The ordinate of the normal distribution is density, the ordinate for behavior problems is frequency
Each of the previous choices is correct
If behavior problem scores are normally distributed, and we want to say something meaningful about what values are likely and what are unlikely, we would have to know
The mean
The standard deviation
The sample size
Both a and b
Knowing that data are normally distributed allows me to
Calculate the probability of obtaining a score greater than some specified value
Calculate the probability of obtaining a score of exactly
Calculate what ranges of values are unlikely to occur by chance
Both a and c
The symbol p is commonly used to refer to
Any value for the observed variable
A value from a standard normal distribution
The probability for the occurrence of an observation
None of the above
A linear transformation of data
Multiplies all scores by a constant and/or adds some constant to all scores
Is illegal
Drastically changes the shape of a distribution
Causes the data to form a straight line
If behavior problem scores are roughly normally distributed in the population, a sample of behavior problems scores will
Be normally distributed with any size sample
More closely resemble a normal distribution as the sample size increases
Have a mean of 0 and a standard deviation of 1
Be negatively skewed
If we know that the probability for z > 1.5 is .067, then we can sa that
The probability of exceeding the mean by more than 1.5 standard deviations is .067
The probability of being more than 1.5 standard deviations away from the mean is .134
86% of the scores are less than 1.5 standard deviations from the mean
All of the above
The text discussed setting "probable limits" on an observation. These limits are those which have a
50% chance of enclosing the value that the observation will have
75% chance of enclosing the value that the observation will have
80% chance of enclosing the value that the observation will have
95% chance of enclosing the value that the observation will have
The formula for calculating the 95% probable limits on an observation is
(μ > 1.96σ)
(σ + 1.96μ)
(μ - 1.96σ)
(μ±1.96σ)
If we have data that have been sampled from a population that is normally distributed with a mean of 50 and a standard deviation of 10, we would expet that 95% of our observations would lie in the interval that is approximately
30-70
35-50
45-55
70-90
The difference between "probable limits" and "confidence limits" is that the probable limits
Focus on estimating where a particular score is likely to lie using a known population mean
Estimate the kinds of means that we expect
Try to set limits that have a .95 probability of containing the population mean
There is no difference
Stanine scores
Are badly skeewed
Have a mean of 5 and cary between 1 and 9
Are always integers
Both b and c
Which of the following is not always true of a normal distribution?
It is symmetric
It has a mean of 0
It is unimodal
Both a and b
"Abscissa" is to _________ as "ordinate" is to ___________.
Density; frequency
Frequency; density
Horizontal; verticle
Verticle; horizontal
The difference between a normal distribution and a standard normal distribution is
Standard normal distributions are more symmetric
Normal distributions are based on fewer scores
Standard normal distributions always have a mean of 0 and a standard deviation of 1
There is no difference
The most common situation in statistical procedures is to assume that
Data are positively skewed
Data are negatively skewed
Data are normally distributed
It doesn't make any difference what the distribution of the data looks like
A normal distribution
Has more than half of its data points to the left of the median
Has more than half of its data points to the right of the mean
Has 95% of its data points within one standard deviation of the mean
Is symmetrical
One of the problems we face when we try to draw conclusions from data is that we have to deal with
Means
Error variance
Population size
Hypotheses
In hypothesis testing our job would be much easier if
Sample statistics accurately reflected population parameters
Subjects didn't vary so much from one another
We knew the population values
All of the above
We are more likely to declare two populations to be different if
The means of our samples are very different
The variability of our samples is very large
The samples are normally distributed
All of the above
If we were to repeat an experiment a large number of times and calculate a statistic such as the mean for each experiment, the distribution of these statistics would be called
The distributional distribution
The error distribution
The sampling distribution
The test outcome
If I calculate the probability of obtaining a particular outcome when the null hypothesis is true, I must deal with
The outcome
A sampling distribution
Conditional probability
All of the above
To look at the sampling distribution of the mean we would
Calculate a mean and compare it to the standard deviation
Calculate a mean and compare it to the standard error
Calculate many means and plot them
Look the sampling distribution up in a book
Sampling distributions help us test hypotheses about means by
Telling us exactly what the population mean is
Telling us how variable the population is
Telling us what kinds of means to expect if the null hypothesis is true
Telling us what kinds of means to expect if the null hypothesis is false
THe basic reason for running an experiment is usually to
Reject the null hypothesis
Reject the experimental hypothesis
Reject the research hypothesis
Find a non-significant difference
Which of the following is a statement of H1
H1 : μ > 0
H1 : μ < 0
H1 : μ ≠ 0
All of the above
Whether or not we reject the null hypothesis depends on
The probability of the result given the null hypothesis is true
How far the data depart from what we would expect if the null hypothesis were true
The size of some test statistic
All of the above
Most psychological research is undertaken with the hope of
Proving the null hypothesis
Proving the alternative hypothesis
Rejecting the null hypothesis
Discovering ultimate truth
The difference between a test comparing two means and a test comparing the frequency of two outcomes is
The test statistics that they employ and their calculation
The logic behind the two different hypothesis testing procedures
The way we go about drawing conclusions from the tests
All of the above
To reject a null hypothesis for the finger tapping example in the text, we would
Calculate the probability of that result if the null hypothesis were false
Calculate the probability of that result if the null hypothesis were true
Compare the probabilities of that result if the null hypothesis were true and if it were false
Reject the null hypothesis unless that subject closely resembled normal subjects
The area that encompasses the extreme 5% of a distribution is frequently referred to as
The retention region
The rejection region
The decision region
None of the above
A Type II error refers to
Rejecting a true null hypothesis
Rejecting a false null hypothesis
Failing to reject a true null hypothesis
Failing to reject a false null hypothesis
We would like to
Maximize the power of a test.
Minimize the probability of a type I error.
Do both a and b
Maximize the probability of a type II error.
A two-tailed test is _______________ powerful than a one-tailed test if we are sure the difference is in the direction that we would have predicted.
More
Less
Equally
We cannot tell
If we erroneously conclude that motorists are more likely to honk at low status cars than high status cars, we
Have made a Type I error
Have made a type II error
Would have made that conclusion 5% of the time if the null hypothesis were true
Both a and c
A researcher was interested in seeing if males or females in large lecture classes fell asleep more during in-class video. The null hypothesis of this study is
Males will fall asleep more than females
Females will fall asleep more than males
Males and females fall asleep at the same rate
More information is needed
The null hypothesis is the statement that
Population means are equal
Population means differ between groups
It is the hypothesis you generally hope to prove
Exciting things are going on
After running a t-test on the mean numbers of jelly beans that men and women eat over the course of the year, I conclude that men eat significantly more jelly beans than women. If men and women actually eat the same number of jelly beans, my conclusion is
A valid conclusion
A Type I error
A Type II error
An example of power
The probability of not rejecting a false null hypothesis is also known as
Type II error
Type I error
Alpha
Both b and c
The probability of not rejecting a null hypothesis when it is false is called?
A type I error
A type II error
Experimenter error
Method error
A type I error has occurred if we
Reject a null hypothesis that is really false
Retain a null hypothesis that is really false
Retain a null hypothesis that is really true
Reject a null hypothesis that is really true
I want to test the hypothesis that children who experience daycare before the age of 3 do better in school than those who do not experience daycare. I have just described the
Alternative hypothesis
Research hypothesis
Experimental hypothesis
All of the above
When we are using a two-tailed hypothesis test, the alternative hypothesis is of the form
H1 : μ ≠ 50
H1 : μ < 50
H1 : μ > 50
H0 : μ = 50
Which of the following is not part of the central limit theorem?
The mean of the sampling distribution approaches the population mean
The variance of the sampling distribution approaches the population variance divided by the sample size
The sampling distribution will approach a normal distribution as the sample size increases
All of the above are part of the central limit theorem
With large samples and a small population variance, the sample means usually
Will be close to the population mean
Will slightly underestimate the population mean
Will slightly overestimate the population mean
Will equal the population mean
The standard error of the mean is
Equal to the standard deviation of the population
Larger than the standard deviation of the population
The standard deviation of the sampling distribution of the mean
None of the above
If the population from which we draw samples is "rectangular" then the sampling distribution of the mean will be
Rectangular
Normal
Bimodal
More normal than the population
Suppose that we know that the sample mean is 18 and the population standard deviation is 3. We want to test the null hypothesis that the population mean is 20. In this situation we would
Reject the null hypothesis at alpha = .05
Reject the null hypothesis at alpha = .01
Retain the null hypothesis
We cannot solve this problem without knowing the sample size
Many textbooks (though not this one) advocate testing the mean of a sample against a hypothesized population mean by using z even if the population standard deviation is now known, so long as the sample size exceeds 30. Those books recommend this because
They don't know any better
There are not tables for t for more than 30 degrees of freedome
The difference between t and z is small for that many cases
T and z are exactly the same for that many cases
The importance of the underlying assumption of normality behind a one-sample means test
Depends on how fussy you are
Depends on the sample size
Depends on whether you are solving for t or z
Doesn't depend on anything
The variance of an individual sample is more likely than not to be
Larger than the corresponding population variance
Smaller than the corresponding population variance
The same as the population variance
Less than the population mean
For a t test with one sample we
Lose one degree of freedom because we have a sample
Lose one degree of freedom because we estimate the population mean
Lose two degrees of freedom because of the mean and the standard deviation
Have n degrees of freedom
If we have run a t test with 35 observations and have found a t of 3.60, which is significant at the .05 level, we would write
T(35) = 3.60, p <.05
T(34) = 3.60, p >.05
T(34) = 3.60, p <.05
T(35) = 3.60, p <05
If we compute 95% confidence limits on the mean as 15-118.4, we can conclude that
The probability is .95 that the sample mean lies between 15 and 118.4
The probability is .05 that the population mean lies between 15 and 118.4
An interval computer in this way has a probability of .95 of bracketing the population mean
The population mean is not less than 15
A 95% confidence interval is going to be __________ a 99% confidence interval
Narrower than
Wider than
The same width as
More accurate than
The two-tailed p value that a statistical program produces refers to
The value of t
The probability of getting at least that large a value of t if the null hypothesis is false
The probability of getting at least that large an absolute value of t if the null hypothesis is true
The probability that the null hypothesis is true
Which of the following statistics comparing a sample mean to a population mean is most likely to be significant if you used a two-tailed test?
T = 10.6
T = 0.9
T = -10.6
Both a and c
A one-sample t test was used to see if a college ski team skied faster than the population of skiers at a popular ski resort. The resulting statistic was t.05 (23) = -7.13, p<.05. What should we conclude?
The sample mean of the college skiers was significantly different from the population mean.
The sample mean of the college skiers was not significantly different from the population mean
The null hypothesis was true
The sample mean was greater than the population mean
A t test is most often used to
Compare two means
Compare the standard deviations of two sample
Compare many means
None of the above
Cohen's "d" is an example of
A measure of correlation
An r-family measure
A d-family measure
A correlational measure
When you have a single sample and want to compute an effective size measure, the most appropriate denominator is
The variance of the sample
The standard deviation of the sample
The sample size
None of the above
A confidence interval computed for the mean of a single sample
Defines clearly where the population mean falls
Is not as good as a test of some hypothesis
Does not help us decide if there is a significant effect
Is associated with a probability statement about the location of a population mean
The t distribution
Is smoother than the normal distribution
Is quite different from the normal distribution
Approaches the normal distribution as its degrees of freedom increase
Is necessary when we know the population standard deviation
The term "effect size" refers to
How large the resulting t statistic is
The size of the p value, or probability associated with that I
The actual magnitude of the mean or difference between means
The value of the null hypothesis
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