Why are normal curves important?

Why are normal curves important?
Choices
A)The normal curve is a special distribution with a specific, unchanging shape that
many samples fall into.
b)Normal curves display a distribution of outcomes that appears in many samples.
c)Every sample of data from the world can be fit into a normal curve.
Based on the normal curve below, what is the likelihood of a randomly selected
person being 70–72 inches tall?
Three differently shaped bell curves illustrate three different normal distributions.
Each of the bell curves is unimodal and symmetrical, two of the characteristics of
normal distributions that can be easily seen in graphs. These curves also show
the effect of the standard deviation on the shape of the bell. The first graph has a
standard deviation of 15, the largest standard deviation, and so its bell is the
widest or broadest in shape. The second graph has a standard deviation of 10
and its bell is narrower in shape. The last graph has a standard deviation of 5. Its
bell curve is the tallest and narrowest.
Choices
a)68%
b)34%
c)50%
Probabilities are reported as decimal proportions in statistics, but they can be
converted to percentages. How would you report 5% as a probability (a decimal
proportion)?
Choices
a)5
b).05
c).5
What is a z score, conceptually?
Choices
a) A z score is a measure of how high the normal curve is at a raw score or
observation.
b) A z score is a measure of how far from the mean a raw score or observation
falls.
c) A z score is a measure of what percentage of values in a normal distribution fall
above a given raw score.
Why are some z scores positive values while others are negative?
Choices
a) Because z scores are assigned to raw values, they are positive if they are
expected and negative if they are outliers.
b) Because z scores measure distance from the mean, a z score can be either
positive (above the mean) or negative (below the mean).
c) 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).
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.
Choices
a) 0.475
b) 0.025
c) There is not enough information to find the answer.
Given M = 14 and s = 4, what is the z score of a raw score of 11?
Choices
a) 0.5
b) −0.75
c) −0.1875
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?
Choices
a) 0.1587
b) 0.3413
c) 1.00
When M = 34 and s = 3, what percentage of scores are lower than 28?
Choices
a) 2.28
b) −2.00
c) 47.72
True or false: Any distribution that is transformed into a z distribution will become
normal.
Choices
a) true
b) False
What do inferential statistics allow researchers to do?
Choices
a) draw conclusions about populations based on sample data
b) describe a sample by computing statistics for it
c) understand how to run inferential statistical tests
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 times is one out of 16, or
6.25 percent. Which of the following assumptions is the best example of “willful
ignorance”?
Choices
a) Both decks contain all 52 cards.
b) Both decks are identical.
c) Both decks were shuffled prior to selection.
What is the probability of selecting a spade from a deck of 52 cards?
Choices
a) 0.33
b) 0.02
c) 0.25
Why is random sampling so important in inferential statistics?
Choices
a) Random sampling is the quickest way to gather data for inferential statistics.
b) Random sampling allows researchers to adjust their samples to make them
adhere more closely to the population.
c) Random sampling maximizes the likelihood that a sample is representative of
the population.
A researcher studies a random sample of U.S. college students and finds that the
average student loan debt is $30,270. Why would it be inappropriate to use this figure
to make inferences about college student debt in Europe?
Choices
a) Some European countries have free college education.
b) European college students were not part of the population the researcher
studied.
c) European countries use different currencies than the U.S.
Why do researchers use hypothesis testing?
Choices
a) to infer information about a population
b) to find useful areas of research from the existing findings
c) to establish the credibility of a given hypothesis about a population
What is a statistical hypothesis?
Choices
a) a formal statement or expectation about the outcome of a study
b) a statement about what is true of a population
c) a numerical statement about the outcome of a study
What is a null hypothesis?
Choices
a) a hypothesis that states that there is no effect of the independent variable on
the dependent variable
b) a hypothesis that states that there was an error in the research
c) a hypothesis that states that the independent variable has a negative effect on
the dependent variable
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 for this experiment?
Choices
a) The research hypothesis would be that squirrels prefer the genetically modified
nuts to non-modified nuts.
b) The research hypothesis would be that the presence of larger squirrels will
cause people to be more interested in the community.
c) The research hypothesis would be that squirrels that eat the genetically
modified nuts will grow to become larger squirrels.
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?
Choices
a) Null hypotheses are not mathematical statements, so rejecting them doesn’t
affect the mathematical alternative hypothesis.
b) The alternative hypothesis is only true if there is enough data to support it.
c) For any inferences made in statistical analysis, researchers have to account for
the probabilistic nature of that conclusion.
How would one construct a theoretical sampling distribution of means?
Choices
a) by choosing a parameter, then measuring for that parameter across every
population
b) by taking samples of every size from a population, then measuring each for a
particular parameter
c) by choosing a sample size, then taking every possible sample of that size from
the population and measuring each for a particular parameter
According to the central limit theorem, when could a sampling distribution NOT be
normal?
Choices
a) A sampling distribution is only normal if the underlying statistic is normally
distributed.
b) A sampling distribution could be non normal when the raw population scores
are wildly nonnormal and the selected sample size is small.
c) A sampling distribution is always normal.
How does the mean of a sampling distribution (of means) compare to the population
mean of the sampled population?
Choices
a) They are equal.
b) The mean of a sampling distribution (of means) is based on random samples,
so it is often slightly different from the overall population mean.
c) The mean of a sampling distribution (of means) is always slightly different from
the population mean.
How is the variability of a sampling distribution affected by the sample size?
Choices
a) The variability of a sampling distribution is not affected by the sample size.
b) The variability of a sampling distribution decreases as the sample size
decreases.
c) The variability of a sampling distribution decreases as the sample size
increases.
Why is there not just one sampling distribution for a given population?
Choices
a) There are as many sampling distributions as there are sample sizes.
b) Sampling distributions can vary depending on which samples are selected
when the distribution is created.
c) There are as many sampling distributions as there are samples.
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″)?
Choices
a) n = 4
b) n = 30
c) Either. Sample size does not impact the likelihood of observing a particular
sample mean.
What is a sampling error?
Choices
a) the difference between two sequential samples’ parameters
b) the difference between a population parameter and the estimate of that
parameter provided by a statistic
c) a mistake made when sampling a population
When should a researcher use a z test instead of a t test?
Choices
a) when the researcher is working directly with the population
b) when the population standard deviation is unknown
c) when the population standard deviation is known
What do z tests and t tests help the researcher decide?
Choices
a) if a sample mean likely comes from a specified population
b) how close a sample mean is to the population mean
c) whether the researcher chose the correct null hypothesis
Why are z scores useful to researchers?
Choices
a) Z scores measure how far a score is from the population parameter by a
standard measure.
b) Z scores measure how precise a given sample is to a population.
c) Z scores determine how much a sample represents a population.
What is the z statistic?
Choices
a) The z statistic is the z score of the actual population.
b) The z statistic is the average z score for all samples in a sampling distribution.
c) The z statistic transforms means within a sampling distribution into z scores.
Z tests involve transforming a sample’s mean into a z statistic. Why is this helpful to
the researcher?
Choices
a) The z statistic shows how unlikely it is that the researcher will reject the null
hypothesis.
b) The z statistic shows how likely the sample is to confirm the null hypothesis.
c) The z statistic shows how unlikely selecting that sample would be, assuming
the null hypothesis is true.
What does it mean that a hypothesis test is a test of a theoretical population?
Choices
a) When hypothesis testing, setting up a theoretical population allows the
researcher to compare their sample against something that better corresponds
to the sample.
b) When hypothesis testing, the researcher 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.
c) When hypothesis testing, the researcher considers a theoretical population that
is identical to the existing population, to see if their experiment has any effect.
Choose the best answer from the options below and fill in the blank: The farther a z
statistic is from 0, ________.
Choices
a) the more a researcher should doubt their experiment procedure
b) the more likely it is that the null hypothesis should be rejected
c) the less likely it is that the null hypothesis should be rejected
For a hypothesis test, a researcher decides to use an alpha level of .10. What does
this mean?
Choices
a) The researcher will reject 10% of the samples and only experiment with the
remaining 90%.
b) 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.
c) 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.
An alpha level of .025 corresponds to the critical values of -1.96 and +1.96. Why are
these critical values important?
Choices
a) Z statistics above +1.96 and below -1.96 belong to samples that are less than
.025 = 2.5% likely, assuming the null hypothesis is true.
b) Critical values are the numbers a sample’s z statistic must be between for a
researcher to reject the null hypothesis.
c) A sample’s z statistic must be between these numbers for the researcher to
consider it in the experiment.
What is statistical significance?
Choices
a) A hypothesis test’s findings are statistically significant when they suggest that
the researcher should reject the null hypothesis.
b) Statistical significance is the process by which a researcher tweaks their alpha
level so that their hypothesis test yields a result.
c) Statistical significance is when a hypothesis test yields a conclusion that will
affect scientific literature.
A researcher hypothesizes that a driving course is effective at preventing vehicle
accidents and decides to test their hypothesis with a z test. The researcher takes a
sample of the driving population, gives them the course, and measures the number of
wrecks they have in a year. 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 took the course yields 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?
Choices
a) The researcher should reject the null hypothesis that the theoretical population
of all drivers who receive this intervention have the same number of accidents
as existing drivers.
b) The researcher should fail to reject the null hypothesis that the theoretical
population of all drivers who receive this intervention have the same number of
accidents as existing drivers.
c) The researcher should take another sample, since a z statistic of -2.5 is very
unlikely.
When should a single sample t test be used instead of a z test?
Choices
a) t tests should be used if a researcher wants to study the whole population,
rather than only samples from the population.
b) t tests should be used when the population standard deviation is unknown.
c) t tests should be used when the population standard deviation is known.
Why is Cohen’s d useful to experimental researchers?
Choices
a) Cohen’s d provides a measure of the frequency with which a researcher may
expect a given z or t score.
b) Cohen’s d provides a standard measure for effect size.
c) Cohen’s d provides a measure of how likely the alternative hypothesis is to be
true.
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?
Choices
a) If there is a restriction, then after selecting a number of things, one will know
what the remaining things are.
b) A restriction on selection results in 0 degrees of freedom.
c) Every restriction removes one degree of freedom.
Which of the following are three important aspects of the outcome of any inferential
test?
Choices
a) An outcome of an inferential test is evidence that is statistical and proof of a
conclusion.
b) An outcome of an inferential test is an opinion that is logical and suggestive of
a conclusion.
c) An outcome of an inferential test is evidence that is statistical and suggestive of
a conclusion.
Just as in other statistical methods, single-sample z and t tests assume that any
samples a researcher gathers have which property?
Choices
a) inclusion
b) randomness
c) representativeness

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