MATH 1680/ 317 Qs with Certified Ans/ 2025
What is at the "heart" of hypothesis testing in statistics? - (answers)Make an assumption about
reality, and collect sample evidence to determine whether it contradicts the assumption.
What is a hypothesis? - (answers)A statement regarding a characteristic of one or more
populations.
Why do we test statements about a population parameter using sample data? - (answers)Because
it is usually impossible or impractical to gain access to the entire population.
State the definition of hypothesis testing. - (answers)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. - (answers)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. - (answers)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.
List the three ways to set up the null and alternative hypotheses. - (answers)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? - (answers)Left and right tailed tests
What determines the structure of the alternative hypothesis (two-tailed, left-tailed, or right-
tailed?) - (answers)The statement we are trying to gather evidence for.
What type of error is called a Type I error? - (answers)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? - (answers)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? - (answers)Null hypothesis: innocent
Alternative hypothesis: guilty
What jury decision is associated with rejecting the null hypothesis? - (answers)Guilty
What jury decision is associated with failing to reject the null hypothesis? - (answers)Not guilty
Is the null hypothesis ever declared "true"? - (answers)No, it is either rejected or not rejected
,In a jury trial, what decision is equivalent to making a Type I error? - (answers)Declaring an
innocent person guilty
In a jury trial, what decision is equivalent to making a Type II error? - (answers)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? - (answers)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? - (answers)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? - (answers)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 - (answers)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, we are
content to recognize the inverse relation between α and β. (As one goes up, the other goes down.
It is important to recognize that we never accept the null hypothesis. - (answers)Sample evidence
can never prove the null hypothesis to be true. By not rejecting the null hypothesis, we are saying
that the evidence indicates that the null hypothesis could be true or that the sample evidence is
consistent with the statement in the null hypothesis.
If the consequences of making a Type I error are severe, would you choose the level of
significance,
α,
, to equal 0.01, 0.05, or 0.10? - (answers)0.01
Give the definition of what it means for a result to be statistically significant. - (answers)When
observed results are unlikely under the assumption that the null hypothesis is true, we say that
the result is statistically significant and we reject the statement in the null hypothesis.
A criterion for testing hypotheses is to determine how likely the observed sample proportion is: -
(answers)under the assumption that the statement in the null hypothesis is true.
Give the definition of a P-value. - (answers)A P-value is the probability of observing a sample
statistic as extreme as or more extreme than one observed under the assumption that the
statement in the null hypothesis is true. Stated another way, the P-value is the likelihood or
probability that a sample will result in a statistic such as the one obtained if the null hypothesis is
true.
Explain how to determine whether the null hypothesis should be rejected using the P-value
approach. - (answers)If the probability of getting a sample statistic as extreme as or more
extreme than the one obtained is small under the assumption that the statement in the null
hypothesis is true, reject the null hypothesis.
What are the three conditions that must be satisfied before testing a hypothesis regarding a
population proportion, p? - (answers)the sample is obtained by simple random sampling or the
data result from a randomized experiment ; np0(1−p0)≥10 where p0 is the proportion stated in
the null hypothesis; and the sampled values are independent of each other. This means that the
sample size is no more than 5% of the population size (n≤0.05N).
State the five steps for testing a hypothesis about a population proportion, p. - (answers)Step 1:
Determine the null and alternative hypotheses. The hypotheses can be structured in one of three
ways:
Step 2: Select a level of significance, α, depending on the seriousness of making a Type I error .
Step 3 (By Hand) Step 3 (Using Technology): compute the test statistic
What is at the "heart" of hypothesis testing in statistics? - (answers)Make an assumption about
reality, and collect sample evidence to determine whether it contradicts the assumption.
What is a hypothesis? - (answers)A statement regarding a characteristic of one or more
populations.
Why do we test statements about a population parameter using sample data? - (answers)Because
it is usually impossible or impractical to gain access to the entire population.
State the definition of hypothesis testing. - (answers)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. - (answers)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. - (answers)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.
List the three ways to set up the null and alternative hypotheses. - (answers)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? - (answers)Left and right tailed tests
What determines the structure of the alternative hypothesis (two-tailed, left-tailed, or right-
tailed?) - (answers)The statement we are trying to gather evidence for.
What type of error is called a Type I error? - (answers)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? - (answers)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? - (answers)Null hypothesis: innocent
Alternative hypothesis: guilty
What jury decision is associated with rejecting the null hypothesis? - (answers)Guilty
What jury decision is associated with failing to reject the null hypothesis? - (answers)Not guilty
Is the null hypothesis ever declared "true"? - (answers)No, it is either rejected or not rejected
,In a jury trial, what decision is equivalent to making a Type I error? - (answers)Declaring an
innocent person guilty
In a jury trial, what decision is equivalent to making a Type II error? - (answers)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? - (answers)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? - (answers)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? - (answers)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 - (answers)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, we are
content to recognize the inverse relation between α and β. (As one goes up, the other goes down.
It is important to recognize that we never accept the null hypothesis. - (answers)Sample evidence
can never prove the null hypothesis to be true. By not rejecting the null hypothesis, we are saying
that the evidence indicates that the null hypothesis could be true or that the sample evidence is
consistent with the statement in the null hypothesis.
If the consequences of making a Type I error are severe, would you choose the level of
significance,
α,
, to equal 0.01, 0.05, or 0.10? - (answers)0.01
Give the definition of what it means for a result to be statistically significant. - (answers)When
observed results are unlikely under the assumption that the null hypothesis is true, we say that
the result is statistically significant and we reject the statement in the null hypothesis.
A criterion for testing hypotheses is to determine how likely the observed sample proportion is: -
(answers)under the assumption that the statement in the null hypothesis is true.
Give the definition of a P-value. - (answers)A P-value is the probability of observing a sample
statistic as extreme as or more extreme than one observed under the assumption that the
statement in the null hypothesis is true. Stated another way, the P-value is the likelihood or
probability that a sample will result in a statistic such as the one obtained if the null hypothesis is
true.
Explain how to determine whether the null hypothesis should be rejected using the P-value
approach. - (answers)If the probability of getting a sample statistic as extreme as or more
extreme than the one obtained is small under the assumption that the statement in the null
hypothesis is true, reject the null hypothesis.
What are the three conditions that must be satisfied before testing a hypothesis regarding a
population proportion, p? - (answers)the sample is obtained by simple random sampling or the
data result from a randomized experiment ; np0(1−p0)≥10 where p0 is the proportion stated in
the null hypothesis; and the sampled values are independent of each other. This means that the
sample size is no more than 5% of the population size (n≤0.05N).
State the five steps for testing a hypothesis about a population proportion, p. - (answers)Step 1:
Determine the null and alternative hypotheses. The hypotheses can be structured in one of three
ways:
Step 2: Select a level of significance, α, depending on the seriousness of making a Type I error .
Step 3 (By Hand) Step 3 (Using Technology): compute the test statistic
