1
MATH 1680/ actual exam Questions with Certified
Answers/ 2025 guaranteed pass
What is at the "heart" of hypothesis testing in statistics? - (answer)Make an
assumption about reality, and collect sample evidence to determine whether it
contradicts the assumption.
What is a hypothesis? - (answer)A statement regarding a characteristic of one or
more populations.
Why do we test statements about a population parameter using sample data? -
(answer)Because it is usually impossible or impractical to gain access to the entire
population.
State the definition of hypothesis testing. - (answer)A procedure based on sample
evidence and probability, used to test statements regarding a characteristic of
one or more populations.
List the 3 steps in hypothesis testing. - (answer)1. Make a statement regarding the
nature of the population.
2. Collect evidence (sample data) to test the statement
3. Analyze the data to assess the plausibility of the statement
State the definition of the null hypothesis. - (answer)A statement to be tested.
The null hypothesis is a statement of no change, no effect, or no difference and is
assumed true until evidence indicates otherwise.
, 2
List the three ways to set up the null and alternative hypotheses. - (answer)Two
tailed test
Equal versus not equal hypothesis
H0 : parameter = some value
H1 : parameter does not equal some value
Left-tailed test
2. Equal versus less than
H0 : parameter = some value
H1 : parameter < some value
Right-tailed test
3. Equal versus greater than
H0 : parameter = some value
H1 : parameter > some value
What type of tests are referred to as one-tailed tests? - (answer)Left and right
tailed tests
, 3
What determines the structure of the alternative hypothesis (two-tailed, left-
tailed, or right-tailed?) - (answer)The statement we are trying to gather evidence
for.
What type of error is called a Type I error? - (answer)Reject the null hypothesis
when the null hypothesis is true. This decision would be incorrect. This type of
error is called a Type I error.
What type of error is called a Type II error? - (answer)Do not reject the null
hypothesis when the alternative hypothesis is true. This decision would be
incorrect. This type of error is called a Type II error.
In a jury trial, what are the null and alternative hypotheses? - (answer)Null
hypothesis: innocent
Alternative hypothesis: guilty
What jury decision is associated with rejecting the null hypothesis? -
(answer)Guilty
What jury decision is associated with failing to reject the null hypothesis? -
(answer)Not guilty
Is the null hypothesis ever declared "true"? - (answer)No, it is either rejected or
not rejected
, 4
In a jury trial, what decision is equivalent to making a Type I error? -
(answer)Declaring an innocent person guilty
In a jury trial, what decision is equivalent to making a Type II error? -
(answer)Declaring a guilty person "not guilty"
What symbols do we use to denote the probability of making a Type I error and
the probability of making a Type II error? - (answer)α = P(Type I error)=P(rejecting
H0 when H0 is true)
β=P(Type II error) = P(not rejecting H0 when H1 is true)
What does the level of significance represent? - (answer)The level of significance,
α, is the probability of making a Type I error
What does the choice of the level of significance depend on? - (answer)The choice
of the level of significance depends on the consequences of making a Type I error.
If the consequences are severe, the level of significance should be small (say,
α=0.01). However, if the consequences are not severe, a higher level of
significance can be chosen (say, α=0.05 or α=0.10).
Why is the level of significance not always set at α=0.01 - (answer)Reducing the
probability of making a Type I error increases the probability of making a Type II
error, β. Using our court analogy from the video explaining Figure 1, a jury is
instructed that the prosecution must provide proof of guilt "beyond all reasonable
doubt." This implies that we are choosing to make α small so that the probability
of convicting an innocent person is very small. The consequence of the small α,
however, is a large β, which means many guilty defendants will go free. For now,
MATH 1680/ actual exam Questions with Certified
Answers/ 2025 guaranteed pass
What is at the "heart" of hypothesis testing in statistics? - (answer)Make an
assumption about reality, and collect sample evidence to determine whether it
contradicts the assumption.
What is a hypothesis? - (answer)A statement regarding a characteristic of one or
more populations.
Why do we test statements about a population parameter using sample data? -
(answer)Because it is usually impossible or impractical to gain access to the entire
population.
State the definition of hypothesis testing. - (answer)A procedure based on sample
evidence and probability, used to test statements regarding a characteristic of
one or more populations.
List the 3 steps in hypothesis testing. - (answer)1. Make a statement regarding the
nature of the population.
2. Collect evidence (sample data) to test the statement
3. Analyze the data to assess the plausibility of the statement
State the definition of the null hypothesis. - (answer)A statement to be tested.
The null hypothesis is a statement of no change, no effect, or no difference and is
assumed true until evidence indicates otherwise.
, 2
List the three ways to set up the null and alternative hypotheses. - (answer)Two
tailed test
Equal versus not equal hypothesis
H0 : parameter = some value
H1 : parameter does not equal some value
Left-tailed test
2. Equal versus less than
H0 : parameter = some value
H1 : parameter < some value
Right-tailed test
3. Equal versus greater than
H0 : parameter = some value
H1 : parameter > some value
What type of tests are referred to as one-tailed tests? - (answer)Left and right
tailed tests
, 3
What determines the structure of the alternative hypothesis (two-tailed, left-
tailed, or right-tailed?) - (answer)The statement we are trying to gather evidence
for.
What type of error is called a Type I error? - (answer)Reject the null hypothesis
when the null hypothesis is true. This decision would be incorrect. This type of
error is called a Type I error.
What type of error is called a Type II error? - (answer)Do not reject the null
hypothesis when the alternative hypothesis is true. This decision would be
incorrect. This type of error is called a Type II error.
In a jury trial, what are the null and alternative hypotheses? - (answer)Null
hypothesis: innocent
Alternative hypothesis: guilty
What jury decision is associated with rejecting the null hypothesis? -
(answer)Guilty
What jury decision is associated with failing to reject the null hypothesis? -
(answer)Not guilty
Is the null hypothesis ever declared "true"? - (answer)No, it is either rejected or
not rejected
, 4
In a jury trial, what decision is equivalent to making a Type I error? -
(answer)Declaring an innocent person guilty
In a jury trial, what decision is equivalent to making a Type II error? -
(answer)Declaring a guilty person "not guilty"
What symbols do we use to denote the probability of making a Type I error and
the probability of making a Type II error? - (answer)α = P(Type I error)=P(rejecting
H0 when H0 is true)
β=P(Type II error) = P(not rejecting H0 when H1 is true)
What does the level of significance represent? - (answer)The level of significance,
α, is the probability of making a Type I error
What does the choice of the level of significance depend on? - (answer)The choice
of the level of significance depends on the consequences of making a Type I error.
If the consequences are severe, the level of significance should be small (say,
α=0.01). However, if the consequences are not severe, a higher level of
significance can be chosen (say, α=0.05 or α=0.10).
Why is the level of significance not always set at α=0.01 - (answer)Reducing the
probability of making a Type I error increases the probability of making a Type II
error, β. Using our court analogy from the video explaining Figure 1, a jury is
instructed that the prosecution must provide proof of guilt "beyond all reasonable
doubt." This implies that we are choosing to make α small so that the probability
of convicting an innocent person is very small. The consequence of the small α,
however, is a large β, which means many guilty defendants will go free. For now,
