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Chapter 3- Displaying Data

For the following set of data [5 9 5 5 2 4] the mean is

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(X_i=mode) > p(X_j= 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

0.667

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.

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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