What is the purpose of a hypothesis test?

To show that there is very little probability that the null is true.

What is a null hypothesis?

The opposite of what the researcher believes; it would nullify their theory

What does the law of large numbers state?

As N larger, the sample mean varies less from the population mean

What is the power of a test?

The probability of rejecting a null hypothesis when it is really false.

What is a test statistic?

A statistic calculated from the data with a known H0 sampling distribution.

What is the critical region of a test?

The values of the test statistic that lead to rejecting the H0.

What does the notation X ~ Binomial(θ, N) represent?

X is a random variable from a binomial distribution

Why is it important to estimate population parameters?

It efficient to draw conclusions about a population based on a sample.

The smallest Type I error rate (α) you are willing to tolerate to reject H0

What is simple random sampling?

A procedure where all the population has equal chance of being selected.

In probability theory, the _____ is assumed to be known, whereas in statistics we have the ____ and work from there.

The model of the world, the data

What is a key characteristic of continuous distributions?

They can take any value within a range.

What is a sampling distribution?

The distribution of specific sample statistic.

What is a sampling distribution of the test statistic?

The distribution of the test statistic under the assumption the H0 is true.

What is the significance level (α) of a test?

The probability of rejecting a null hypothesis when it is actually true.

What is the Bayesian view of probability?

Degree of belief informed by data and exiting knowledge

What is a confidence interval?

A range of values within which the sample mean will land in 95% of samples.

If a study yields a p-value of 0.01, what does this mean?

The probability of making a Type I error is 0.01.

What are the parameters of the binomial distribution?

theta (probability of success for a single trial) and number of trials

What is the law of total probability?

The sum of all probabilities in a sample space is 1

What is the primary goal of hypothesis testing?

To establish whether the data support a theory by rejecting its rival.

What is the relationship between the area under the curve and probability in a continuous distribution?

The area under the curve represents the probability.

What is the standard error?

The standard deviation of the sampling distribution.

In hypothesis testing, what is the difference between a research hypothesis and a statistical hypothesis?

Research hypothesis = psychology, Statistical = data generating mechanism.

What does the central limit theorem state?

As N increases, the sampling distribution of the mean becomes more normal

What is a population parameter?

A characteristic of the entire population.

In the context of hypothesis testing, what is a Type I error?

Rejecting a null hypothesis that is actually true.

What does "probability density" represent?

The height of the curve in a continuous distribution

What is a population in statistics?

The set of all possible people or observations of interest.

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Answers

1
What is the purpose of a hypothesis test?
To prove that the null hypothesis is true.
To confuse statistics students.
To show that there is very little probability that the null is true.
To prove that the alternative hypothesis is true.
2
What is the frequentist view of probability?
Rational gambling
Long-run frequency
Subjective probability
Degree of belief
3
What is a null hypothesis?
The hypothesis that is probably true.
The hypothesis that the researcher wants to believe.
The opposite of what the researcher believes; it would nullify their theory
The alternative hypothesis.
4
What are the parameters of the normal distribution?
x and q
p and n
mean and sd
size and probability
5
What does the law of large numbers state?
The population mean approaches infinity as the sample size increases.
As N gets smaller, the sample mean varies less from the population mean.
As N larger, the sample mean varies less from the population mean
The sample mean approaches zero as the sample size increases.
6
What is the power of a test?
The probability of a Type I error.
The significance level of the test.
The probability of rejecting a null hypothesis when it is really false.
The probability of retaining a true null hypothesis.
7
What is a test statistic?
The ratio of Type I to Type II error.
The central tendency and variability in the population.
A statistic calculated from the data with a known H0 sampling distribution.
A characteristic of the population stated statistically.
8
What is the critical region of a test?
The values of the test statistic that lead to rejecting the H0.
The values of the test statistic that lead to retaining the H0.
The range of acceptable p-values.
The region where the null hypothesis is actually true.
9
What does the notation X ~ Binomial(θ, N) represent?
X is a probability model
X is a random variable from a binomial distribution
X is a sample space
X is a statistical inference
10
Why is it important to estimate population parameters?
It efficient to draw conclusions about a population based on a sample.
Because population parameters are always unknown.
Because sample statistics are more accurate than population parameters.
It is not important.
11
What is a p-value?
The probability that the null hypothesis is true.
The probability that the alternative hypothesis is true.
The smallest Type I error rate (α) you are willing to tolerate to reject H0
The largest Type I error rate (α) you are willing to tolerate to reject H0
12
What is simple random sampling?
A procedure where all the population has equal chance of being selected.
A procedure where important members of the population are selected
Selecting a sample in a way that is convenient to the researcher.
Sampling from a hidden or hard-to-access population.
13
In probability theory, the _____ is assumed to be known, whereas in statistics we have the ____ and work from there.
The statistical inference, the mathematical laws
The data, the model of the world
The conclusions, the inferences
The model of the world, the data
14
What is a key characteristic of continuous distributions?
They can take any value within a range.
They have gaps between values.
They have discrete values.
Probabilities are calculated for specific outcomes.
15
What is a sampling distribution?
The distribution of the population.
The distribution of a sample.
The distribution of specific sample statistic.
A distribution of population parameters.
16
What is a sampling distribution of the test statistic?
The distribution of the population parameter.
The distribution of the test statistic under the assumption the H0 is true.
The distribution of the data under the assumption the H1 is true.
The distribution of the sample data.
17
What is the significance level (α) of a test?
The probability of a Type II error.
The power of the test.
The probability of rejecting a null hypothesis when it is actually true.
The probability of retaining a false null hypothesis.
18
What is the Bayesian view of probability?
Long-run frequency
Objective probability
Relative frequency
Degree of belief informed by data and exiting knowledge
19
What is the sample space?
A set of statistical inferences
A set of probabilities
A set of possible events
A set of data points
20
What is a confidence interval?
A range of values that is certain to contain the true population parameter.
A single value estimate of a population parameter.
The range within which 95% of the population values are found
A range of values within which the sample mean will land in 95% of samples.
21
If a study yields a p-value of 0.01, what does this mean?
The probability that the null hypothesis is true is 0.01.
The probability of making a Type I error is 0.01.
The probability of making a Type II error is 1 - 0.01 (99%)
The probability that the alternative hypothesis is false is 0.01.
22
What are the parameters of the binomial distribution?
mean and sample size
number of trials and the constant c
theta (overall probability of success) and number of options
theta (probability of success for a single trial) and number of trials
23
What is the law of total probability?
The probability of an event is always 1
The sum of all probabilities in a sample space is 0
The sum of all probabilities in a sample space is 1
The probability of an event is always 0.5
24
What is the primary goal of hypothesis testing?
To confuse the public and make researchers look sophisticated
To calculate the probability of the null hypothesis.
To prove that a theory is true.
To establish whether the data support a theory by rejecting its rival.
25
What is the name of the mathematician that the commonly used probability approach is based on?
Fisher
Kolmogorov
Meehl
Bayes
26
What is the range of probability values?
0 to 1
0 to 100
-ve infinity to +ve infinity
-1 to 1
27
What is the relationship between the area under the curve and probability in a continuous distribution?
The area under the curve represents the probability.
There is no relationship.
The area above the curve represents the probability.
The height of the curve represents the probability.
28
What is the standard error?
The mean of the sampling distribution.
The mean of the sample.
The standard deviation of the sampling distribution.
The standard deviation of the population.
29
What does P(head) = 0.5 represent in the context of a coin flip?
Data analysis
Experimental design
Statistical inference
Probability model
30
What percentage of the area under a standard normal distribution falls within 1 standard deviation of the mean?
68.3%
95.4%
99.7%
50%
31
In hypothesis testing, what is the difference between a research hypothesis and a statistical hypothesis?
A statistical hypothesis is a claim about psychological constructs.
They are the same thing, one just looks more complicated.
Research hypothesis = psychology, Statistical = data generating mechanism.
A research hypothesis is mathematically precise.
32
What does the central limit theorem state?
The mean of the sampling distribution is different from the μ
The sampling distribution of the mean is always normal.
As N increases, the sampling distribution of the mean becomes more normal
The population distribution shape determines sampling distribution shape.
33
In the binomial distribution, what does 'N' represent?
Success probability
Number of successes
Number of trials
Probability of failure
34
In the binomial distribution, what does 'θ' represent?
Success probability
Total probability
Number of trials
Number of successes
35
What is a population parameter?
A variable calculated from the sample data.
The estimate of the population mean.
A characteristic of a sample.
A characteristic of the entire population.
36
In the context of hypothesis testing, what is a Type I error?
Rejecting a null hypothesis that is actually true.
Retaining a null hypothesis that is actually false.
Accepting the alternative hypothesis.
Failing to reject the null hypothesis.
37
What does "probability density" represent?
The area under the curve in a continuous distribution
The cumulative probability in a continuous distribution
The height of the curve in a continuous distribution
The probability of a specific outcome in a continuous distribution
38
What is a population in statistics?
The set of all possible people or observations of interest.
The average of a sample.
A subset of data.
A concrete set of data.
39
Which R function is used to generate random numbers from a normal distribution?
pnorm()
dnorm()
qnorm()
rnorm()

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