Hypothesis Testing, Introduction to Linear Regression
Questions with Correct Answers 2025
What is a hypothesis? - correct answers-This is a statement about a population for the purpose of
statistical testing. All hypothesis tests involve making statements about population parameters, or
population distributions, and testing those statements based on samples taken from the population to
see whether the statements are true or not.
What are the (7) steps in testing a hypothesis? - correct answers-1. State the Null Hypothesis and the
Alternate Hypothesis
The first step is to state the null hypothesis (designated as H0) which is the statement that is to be
tested. The null hypothesis is a statement about the value of a population. The null hypothesis will
either be rejected or fail to be rejected.
The alternate hypothesis is the statement that is accepted if the sample data provides insufficient
evidence that the null hypothesis is false. It is designated as H1 and is accepted if the sample data
provides sufficient statistical evidence that H0 is false.
2. Determine the appropriate test statistic and probability distribution.
The test statistic will be of the general form:
test statistic = (sample statistic - parameter value under H0) / standard error of sample statistic
3. Choose the level of significance
The level of significance is the probability of rejected the null hypothesis when it is actually true. Alpha is
used to represent this probability. The significance level is used to choose the probability that a Type 1
error will occur (rejected a true null hypothesis)
4.Formulate the Decision Rule
A decision rule is a statement of the conditions under which the null hypothesis WILL BE rejected and
under which it WILL NOT be rejected.
The critical values (or the rejection points) is the dividing point between the region where the null
hypothesis is rejected and the region whether it is not rejected.
5. Collect Data and Perform Calculations
Once the data has been collected, the test statistic should be calculated
6. Make a Decision
If the test statistic is GREATER THAN the HIGHER CRITICAL VALUE (or in a two-tailed test, LOWER than
the LOWER CRITICAL VALUE), then the null hypothesis is rejected in favor of the alternate.
7. Making Investment Decisions
,Consider the economic effects of statistical decision making
What is the null hypothesis? What is the alternate hypothesis? - correct answers-Null --> This is
designated as H0, and it is the statement that is to be TESTED, it is a STATEMENT about the
POPULATION.
Example--> the mean monthly return for stocks is not significantly different from 1%, there H0: μ = 1%.
Alternate --> This statement, designated as H1, is accepted if the sample data provides sufficient
evidence that the null hypothesis is FALSE.
Example --> Suppose the mean time to market for a new pharmaceutical drug is thought to be 3.9 years.
What are the null and alternate hypotheses. - correct answers-H0: μ = 3.9 years
H1: μ ≠ 3.9 years
What are the (3) basic ways of formulating the null hypothesis? - correct answers-1. H0: μ = μ0 versus
H1: μ ≠ μ0. This hypothesis is two-tailed, which means that you are testing evidence that the actual
parameter may be statistically greater or less than the hypothesized value.
H0: ≤ μ0 versus H1: μ > μ0. This hypothesis is one-tailed; it tests whether there is evidence that the
actual parameter is significantly greater than the hypothesized value. If there is, the null hypothesis is
rejected. If there is not, the null hypothesis is accepted.
H0: μ ≥ μ0 versus H1: μ < μ0. This hypothesis is one-tailed; it tests whether there is evidence that the
actual parameter is significantly less than the hypothesized value. If there is, the null hypothesis is
rejected. If there is not, the null hypothesis is accepted.
What is the general form of a test statistic? What's an example? - correct answers-Test Statistic =
(Sample Statistic - Parameter Value Under H0) / Standard Error of Sample Statistic
For example, a test statistic for a mean of a distribution often follows a standard normal distribution.
Therefore, the test-statistic required will use a z-test P(Z <= test statistic = z). This is shown as:
Test statistic - (X-bar - μ0) / σ√n
Where:
X-Bar: Sample Mean
μ0: Hypothesized Value
σ: Sample Standard Deviation
n: Sample Size
, If we reject a null hypothesis at the 5% level, do we also reject it at the 1% level? - correct answers-
FALSE.
A result may be significant at the 5% level but not at the 1% level. HOWEVER, if we reject at 1%, we
would also reject at 5%.
What are the four possible outcomes in hypothesis testing? - correct answers-1. Reject the null
hypothesis when it's false. This is a correct decision.
2. Incorrectly rejecting the null hypothesis when it's correct. This is known as a TYPE 1 ERROR. The
probability of a Type 1 error is designated by alpha (α).
3. Do not reject the null hypothesis when it's true. This is the correct decision
4. Fail to reject the null hypothesis when it's false. This is known as a TYPE 11 ERROR. The probability of
a Type II Error is designated by beta (β)
What type of error (I, II) is more serious? What is the tradeoff between both error types? How can we
reduce the likelihood of these errors. - correct answers-Of the two errors, TYPE I error is MORE SERIOUS
than TYPE II error.
The tradeoff between Type I and Type II errors is that that you can reduce the probability of Type I error
by choosing a LOW significance level, but this will increase the chance of getting a TYPE II error.
To reduce the probabilities of both types of errors simultaneously, the sample size should be increased.
What are the key words/terms to look for when assessing whether a Type 1 or Type 11 error has
occurred? - correct answers-Type 1- Has to do with the NULL hypothesis- so when we look at "rejecting
the null/H0, or CONCLUDING that..." then we are looking at a Type 1 error description
Type II- Has to do with the fact that the null COULD BE possible, but NO DECISION CAN BE TAKEN TO
REJECT THE NULL. So look for key words like "GOING ALONG WITH..." as an indication of a Type 11 error.
What is the power of test? - correct answers-The probability that a test will CORRECTLY lead to rejecting
the NULL hypothesis for a particular value in the ALTERNATIVE hypothesis.
What is a decision rule? What are critical values (rejection points)? - correct answers-Decision Rule-->
this is a statement of the conditions under which the null hypothesis will be rejected and under which
the null will not be rejected.
Critical Values/Rejection Points--> Dividing points between the region where the null hypothesis is
rejected and the region where it is not rejected.
What is the general decision rule for hypothesis testing, and what do decision rules depend on (2
factors) - correct answers-The general decision rule is that:
1. If the magnitude of the calculated test statistic exceeds the rejection point(s), then the result is
considered statistically significant and the null hypothesis (H0) should be rejected.
2. OTHERWISE, the result IS NOT statistically significant and the null hypothesis (H0) IS NOT rejected.
Questions with Correct Answers 2025
What is a hypothesis? - correct answers-This is a statement about a population for the purpose of
statistical testing. All hypothesis tests involve making statements about population parameters, or
population distributions, and testing those statements based on samples taken from the population to
see whether the statements are true or not.
What are the (7) steps in testing a hypothesis? - correct answers-1. State the Null Hypothesis and the
Alternate Hypothesis
The first step is to state the null hypothesis (designated as H0) which is the statement that is to be
tested. The null hypothesis is a statement about the value of a population. The null hypothesis will
either be rejected or fail to be rejected.
The alternate hypothesis is the statement that is accepted if the sample data provides insufficient
evidence that the null hypothesis is false. It is designated as H1 and is accepted if the sample data
provides sufficient statistical evidence that H0 is false.
2. Determine the appropriate test statistic and probability distribution.
The test statistic will be of the general form:
test statistic = (sample statistic - parameter value under H0) / standard error of sample statistic
3. Choose the level of significance
The level of significance is the probability of rejected the null hypothesis when it is actually true. Alpha is
used to represent this probability. The significance level is used to choose the probability that a Type 1
error will occur (rejected a true null hypothesis)
4.Formulate the Decision Rule
A decision rule is a statement of the conditions under which the null hypothesis WILL BE rejected and
under which it WILL NOT be rejected.
The critical values (or the rejection points) is the dividing point between the region where the null
hypothesis is rejected and the region whether it is not rejected.
5. Collect Data and Perform Calculations
Once the data has been collected, the test statistic should be calculated
6. Make a Decision
If the test statistic is GREATER THAN the HIGHER CRITICAL VALUE (or in a two-tailed test, LOWER than
the LOWER CRITICAL VALUE), then the null hypothesis is rejected in favor of the alternate.
7. Making Investment Decisions
,Consider the economic effects of statistical decision making
What is the null hypothesis? What is the alternate hypothesis? - correct answers-Null --> This is
designated as H0, and it is the statement that is to be TESTED, it is a STATEMENT about the
POPULATION.
Example--> the mean monthly return for stocks is not significantly different from 1%, there H0: μ = 1%.
Alternate --> This statement, designated as H1, is accepted if the sample data provides sufficient
evidence that the null hypothesis is FALSE.
Example --> Suppose the mean time to market for a new pharmaceutical drug is thought to be 3.9 years.
What are the null and alternate hypotheses. - correct answers-H0: μ = 3.9 years
H1: μ ≠ 3.9 years
What are the (3) basic ways of formulating the null hypothesis? - correct answers-1. H0: μ = μ0 versus
H1: μ ≠ μ0. This hypothesis is two-tailed, which means that you are testing evidence that the actual
parameter may be statistically greater or less than the hypothesized value.
H0: ≤ μ0 versus H1: μ > μ0. This hypothesis is one-tailed; it tests whether there is evidence that the
actual parameter is significantly greater than the hypothesized value. If there is, the null hypothesis is
rejected. If there is not, the null hypothesis is accepted.
H0: μ ≥ μ0 versus H1: μ < μ0. This hypothesis is one-tailed; it tests whether there is evidence that the
actual parameter is significantly less than the hypothesized value. If there is, the null hypothesis is
rejected. If there is not, the null hypothesis is accepted.
What is the general form of a test statistic? What's an example? - correct answers-Test Statistic =
(Sample Statistic - Parameter Value Under H0) / Standard Error of Sample Statistic
For example, a test statistic for a mean of a distribution often follows a standard normal distribution.
Therefore, the test-statistic required will use a z-test P(Z <= test statistic = z). This is shown as:
Test statistic - (X-bar - μ0) / σ√n
Where:
X-Bar: Sample Mean
μ0: Hypothesized Value
σ: Sample Standard Deviation
n: Sample Size
, If we reject a null hypothesis at the 5% level, do we also reject it at the 1% level? - correct answers-
FALSE.
A result may be significant at the 5% level but not at the 1% level. HOWEVER, if we reject at 1%, we
would also reject at 5%.
What are the four possible outcomes in hypothesis testing? - correct answers-1. Reject the null
hypothesis when it's false. This is a correct decision.
2. Incorrectly rejecting the null hypothesis when it's correct. This is known as a TYPE 1 ERROR. The
probability of a Type 1 error is designated by alpha (α).
3. Do not reject the null hypothesis when it's true. This is the correct decision
4. Fail to reject the null hypothesis when it's false. This is known as a TYPE 11 ERROR. The probability of
a Type II Error is designated by beta (β)
What type of error (I, II) is more serious? What is the tradeoff between both error types? How can we
reduce the likelihood of these errors. - correct answers-Of the two errors, TYPE I error is MORE SERIOUS
than TYPE II error.
The tradeoff between Type I and Type II errors is that that you can reduce the probability of Type I error
by choosing a LOW significance level, but this will increase the chance of getting a TYPE II error.
To reduce the probabilities of both types of errors simultaneously, the sample size should be increased.
What are the key words/terms to look for when assessing whether a Type 1 or Type 11 error has
occurred? - correct answers-Type 1- Has to do with the NULL hypothesis- so when we look at "rejecting
the null/H0, or CONCLUDING that..." then we are looking at a Type 1 error description
Type II- Has to do with the fact that the null COULD BE possible, but NO DECISION CAN BE TAKEN TO
REJECT THE NULL. So look for key words like "GOING ALONG WITH..." as an indication of a Type 11 error.
What is the power of test? - correct answers-The probability that a test will CORRECTLY lead to rejecting
the NULL hypothesis for a particular value in the ALTERNATIVE hypothesis.
What is a decision rule? What are critical values (rejection points)? - correct answers-Decision Rule-->
this is a statement of the conditions under which the null hypothesis will be rejected and under which
the null will not be rejected.
Critical Values/Rejection Points--> Dividing points between the region where the null hypothesis is
rejected and the region where it is not rejected.
What is the general decision rule for hypothesis testing, and what do decision rules depend on (2
factors) - correct answers-The general decision rule is that:
1. If the magnitude of the calculated test statistic exceeds the rejection point(s), then the result is
considered statistically significant and the null hypothesis (H0) should be rejected.
2. OTHERWISE, the result IS NOT statistically significant and the null hypothesis (H0) IS NOT rejected.
