2 Multiple-Choice Questions
1. Why are normal curves important?
Normal curves display a distribution of outcomes that appears in many samples
Every sample of data from the world can be fit into a normal curve.
The normal curve is a special distribution with a specific, unchanging shape that
many samples fall into.
2. Based on the normal curve below, what is the likelihood of a randomly selected person
being 70-72 inches tall?
68%
34%
50%
Multiple-Choice Question
1. Probabilities are reported as decimal proportions in statistics, but they can be converted to
percentages. How would you report 5% as probability (a decimal proportion)?
.5
.05
5
2 Multiple-Choice Questions
1. What is a z score, conceptually?
A z score is a measure of how high the normal curve is at a raw score or
observation
A z score is a measure of what percentage of values in a normal distribution fall
above a given raw score.
A z score is a measure of how far from the mean a raw score observation falls.
2. Why are some z scores positive values while others are negative?
Because z scores measure distance from the mean, a z score can be either positive
(above the mean) or negative (below the mean).
Because z scores are assigned to raw values, they are positive if they are expected
and negative if they are outliers.
Because z scores reflect how close an observation is to the mean, a z score can
either be positive (very close to the mean) or negative (far from the mean)
Multiple-Choice Question
1. What is the total percentage of scores that lie to the right of the z score of +1.96? Use the
z table in the appendix to find the answer.
0.475
There is not enough information to find the answer.
0.025
Multiple-Choice Question
1. Given M= 14 and s = 4, what is the z score of a raw score of 11?
-0.75
0.5
-0.1875
2 Multiple-Choice Questions
1. Use Formula 3.1b and the z table to solve the problem below.
If a distribution has a mean of 130 and a standard deviation of 10, what is the probability
of randomly selecting a score above 140?
0.1587
0.3413
1.00
2. Use Formula 3.1b and the z table to solve the problem below.
When M=34 and s=3, what percentage of scores are lower than 28?
2.28
-2.00
47.72
Multiple-choice Question
1. True or false: Any distribution that is transformed into a z distribution will become
normal.
True
False
Multiple-Choice Question
1. What do inferential statistics allow researchers to do?
Draw conclusions about populations based on sample data.
Understand how to run inferential statistical tests
Describe a sample by computing statistics for it
Multiple-Choice Question
1. A dealer draws a card from one deck and then draws a card from another deck. A
researcher states that the likelihood of drawing a spade both time is on out of 16, or 6.25
percent. Which of the following assumptions is the best of “willful ignorance”?
Both decks contain all 52 cards
Both decks were shuffled prior to selection
Both decks are identical
Multiple-Choice Question
1. What Is the probability of selecting a spade from a deck of 52 cards?
0.25
0.33
0.02
2 Multiple-Choice Questions
1. Why is random sampling so important in inferential statistics?
Random sampling allows researchers to adjust their samples to make them adhere
more closely to the population.
Random sampling maximizes the likelihood that a sample is representative of the
population.
Random sampling is the quickest way to gather data for inferential statistics.
2. A researcher studies a random sample of U.S. college students and finds that the average
student loan dept is $30,270. Why would it be inappropriate to use this figure to make
inferences about college student debt in Europe?
Some European countries have free college education
European countries use different currencies than the U.S.
European college students were not part of the population the researcher studied
Multiple-Choice Question
1. Why do researchers use hypothesis testing?
To find useful areas of research from the existing findings
To infer information about a population
To establish the credibility of a given hypothesis about a population
3 Multiple-Choice Questions
1. What is a statistical hypothesis?
A numerical statement about the outcome of a study
A formal statement or expectation about the outcome of a study
A statement about what is true of a population
2. What is a null hypothesis?
A hypothesis that states that there was an error in the research
A hypothesis that states that there is no effect of the independent variable on the
dependent variable
A hypothesis that states that the independent variable has a negative effect on the
dependent variable
3. Suppose a local promoter, wanting to create a unique selling feature for their community,
decides to try to create larger squirrels by making and spreading genetically modified
nuts throughout the community that have been supplemented with a growth hormone.
What would the research hypothesis be this experiment?
The research hypothesis would be that the presence of larger squirrels will cause
people to be more interested in the community.
The research hypothesis would be that squirrels that eat the genetically modified
nuts will grow to become larger squirrels.
The research hypothesis would be that squirrels prefer the genetically modified
nuts to non-modified nuts.
Multiple-Choice Question
1. If a statistical analysis suggests the null hypothesis should be rejected, this only means
that the alternative hypothesis is most likely true. Why is this the case?
The alternative hypothesis is only true if there is enough data to support it.
Null hypotheses are not mathematical statements, so rejecting them doesn’t affect
the mathematical alternative hypothesis.
For any inferences made in statistical analysis, researchers have to account for the
probabilistic nature of that conclusion.
Multiple-Choice Question
1. How would one construct a theoretical sampling distribution of means?
By choosing a sample size, then taking every possible sample of that size from the
population and measuring each for a particular parameter.
By taking samples of every size from a population, then measuring each for a
particular parameter.
By choosing a parameter, then measuring for that parameter across every
population.
2 Multiple-Choice Questions
1. According to the central limit theorem, when could a sampling distribution NOT be
normal?
A sampling distribution is always normal.
A sampling distribution could be nonnormal when the raw population scores are
wildly nonnormal and the selected sample size is small.
A sampling distribution is only normal if the underlying statistic is normally
distributed.
2. How does the mean of a sampling distribution (of means) compare to the population
mean of the sampled population?
The mean of a sampling distribution (of means) is always slightly different from
the population mean.
The mean of a sampling distribution (of means) is based on random samples, so it
is often slightly different from the overall population mean.
They are equal.
3 Multiple-Choice Question
1. How is the variability of a sampling distribution affected by the sample size?
The variability of a sampling distribution decreases as the sample size decreases
The variability of a sampling distribution is not affected by the sample size
The variability of a sampling distribution decreases as the sample size increases.
2. Why is there not just one sampling distribution for a given population?
There are as many sampling distributions as there are samples.
Sampling distributions can vary depending on which samples are selected when
the distribution is created.
There are as many sampling distributions as there are sample sizes.
3. The height of a population of high school students from a small city is collected and the
mean is found to be 67 inches (5’7”). In creating the sampling distribution, which sample
size (n) is most likely to produce a sample with a mean of 75 inches (6’3”)
N=30
Either. Sample size does not impact the likelihood of observing a particular
sample mean
N=4
Multiple-Choice Question
1. What is a sampling error?
The difference between two sequential samples’ parameters
A mistake made when sampling a population
The difference between a population parameter and the estimate of that parameter
provided by a statistic.
2 Multiple-Choice Questions
1. When should a researcher use a z test instead of a t test?
When the researcher is working directly with the population
When the population standard deviation is unknown
When the population standard deviation is known
2. What do z tests and t tests help the researcher decide?
How close a sample mean is to the population mean
If a sample mean likely comes from a specified population
Whether the researcher chose the correct null hypothesis
2 Multiple-Choice Questions
1. Why are z scores useful to researchers?
Z scores determine how much a sample represents a population
Z scores measure how precise a given sample is to a population
Z scores measure how far a score is from the population parameter by a standard
measure
2. What is the z statistic?
The z statistic transforms means within a sampling distribution into z scores
The z statistic is the average z score for all samples in a sampling distribution
The z statistic is the z score of the actual population
2 Multiple-Choice Questions
1. Z tests involve transforming a sample’s mean into a z statistic. Why is this helped to the
researcher?
The z statistic shows how likely the sample is to confirm the null hypothesis.
The z statistic shows how unlikely selecting that sample would be, assuming the
null hypothesis true.
The z statistic shows how unlikely it is that the researcher will reject the null
hypothesis.
2. What does it mean that a hypothesis test is a test of a theoretical population?
When hypothesis testing, the researcher considers a theoretical population that is
identical to the existing population, to see if their experiment has any effect.
When hypothesis testing, setting up a theoretical population allows the researcher
to compare their sample against something that better corresponds to the sample.
When hypothesis testing, the researchers is setting up a theoretical population,
which is different from the existing population, and seeing if that difference has
an effect on a specific statistic.
Multiple-Choice Question
1. Choose the best answer from the options below and fill in the black: The farther a z
statistic is from 0,------.
The less likely it is that the null hypothesis should be rejected
The more a researcher should doubt their experiment procedure
The more likely it is that the null hypothesis should be rejected
2 Multiple-Choice Questions
1. For a hypothesis test, a researcher decides to use an alpha level of .10. what does this
mean?
The researcher will reject 10% of the samples and only experiment with the
remaining 90%
The researcher will reject the null hypothesis if the observed sample statistic is
less than or equal to 10% likely (p≤ .10) to occur if the null hypothesis is assumed
to be true.
The researcher will reject the null hypothesis if the observed sample statistic is
more than 10% likely (p>.10) to occur if the null hypothesis is assumed to be true
2. An alpha level of .025 corresponds to the critical values of - 1.96 and +1.96. Why are
these critical values important?
Critical values are the numbers of a samples Z statistics must be between for a
researchers to reject the null hypothesis.
Z statistics above +1.96 and below - 1.96 belong to samples that are less than .025
= 2.5% likely, assuming that null hypothesis is true.
A sample Z statistics must be between these numbers for the researchers to
consider it in the experiment.
2 Multiple-Choice Questions
1. What is statistical significance?
A hypothesis test finding are statistically significant when they suggest that the
researchers should reject the null hypothesis.
Statistical significance is when a hypothesis test yields a conclusion that will
affect scientific literature.
Statistical significance is the process by which a researcher tweaks their alpha
level so their hypothesis test yields a result.
2. A researcher hypothesizes that a driving course is effective at preventing vehicle
accidents and decides to test their hypothesis with A Z test period the researcher takes a
sample of the driving population, gives them the course, and measures the number of rats
they have and they gear. By using data about the entire population of drivers, the
researcher finds a sampling distribution of the mean number of wrecks over a year. The
researcher finds that the sample of drivers who take the course yield A Z statistic of - 2.5
(p= .01). If the critical values were ±1.96 based on an alpha value of 05, what should the
researcher conclude?
The researcher should take another sample, since A Z statistic of - 2.5 is very
unlikely.
The researcher should fail to reject the null hypothesis that they theoretical
population of all drivers who receive this intervention have the same number of
accidents as existing drivers.
The researcher should reject the null hypothesis that the theoretical population of
all drivers who received this intervention have the same number of accidents as
existing drivers.
2 Multiple-Choice Questions
1. When should a single sample T test be used instead of a Z test?
T test should be used if a researcher wants to study the whole population, rather
than only samples from the population.
T test should be used when the population standard deviation is known.
T test should be used when the population standard deviation is unknown.
2. Why is Cohen’s d useful to experimental researchers?
Cohen’s d provides a standard measure for effective size.
Cohen’s d provides a measure of how likely the alternative hypothesis is to be
true.
Cohen’s d provides a measure of the frequency with which a researcher may
expect a given Z or T score.
Multiple-Choice Question
1. Degrees of freedom are always equal to the number of things that are “free” to vary,
unless there is a restriction on those things. Why is this the case?
Every restriction removes one degree of freedom.
If there is a restriction, then after selecting a number of things, one will know
what the remaining things are.
A restriction on selection results in 0 degrees of freedom.
Multiple-Choice Question
1. Which of the following are three important aspects of the outcome of any inferential test?
An outcome of an inferential test is an opinion that is logical and suggestive of a
conclusion.
An outcome of an inferential test is evidence that is statistical and proof of a
conclusion.
An outcome of an inferential test is evidence that is statistical and suggestive of a
conclusion.
Multiple-Choice Question
1. Just as in other statistical methods, single-sample Z and T test assume that any sample
that a researcher gathers have which property?
Inclusion
Randomness
Representativeness
