ECO 391 Exam 2 Questions with Correct Answers Latest Update 2025 Already Passed
Null Hypothesis (H0) - Answers A statement that you will test. A claim of no difference, meaning that
things are the same as each other. Always specifies a value
Example of a Null Hypothesis - Answers H0: Head = 0.5
Alternative Hypothesis (HA) - Answers A hypothesis opposing the null hypotheses. Never specifies a
value
Example of Alternative Hypothesis - Answers HA: Head ≠ 0.5 or Head < 0.5 or Hero > 0.5
What is the reason to conduct hypothesis tests? - Answers To determine if the sample evidence
contradicts the null hypothesis
If we fail to reject the null hypothesis what does it mean? - Answers It doesn't mean that we accept the
null hypothesis
One-tailed hypothesis test - Answers The alternative hypothesis states that the population parameter is
greater than (right-tailed) or less than (left-tailed) the value specified under the null hypothesis
Example of an One-tailed hypothesis test - Answers H0: u = 50
HA: u > 50 (right-tailed) or u < 50 (left-tailed)
Two-tailed hypothesis test - Answers The alternative hypothesis states that the population parameter is
simply different from the one specified under the null
Example of a Two-tailed hypothesis test - Answers H0: u = 50
HA: u ≠ 50
Type 1 Error - Answers Rejecting the null hypothesis when it's actually true
Type 2 Error - Answers Do not reject the null hypothesis when it's actually false
What is an example of a Type 1 Error - Answers When a jury concludes someone is guilty when in reality
they are innocent
What is an example of a Type 2 Error - Answers When a jury concludes is innocent when in reality they
are guilty
What is the equation for standard error? - Answers s/√ n
What is the equation for T-statistic? - Answers T= (x̅-u)/(s/√ n)
Three scenarios for Two-Sample t-Test - Answers 1. When o1 and o2 are known
2. When o1 and o2 are unknown, but equal
, 3. When o1 and o2 are unknown and unequal
Why do we focus on the third scenario for a Two-Sample t-Test - Answers 1. In general, the population
standard deviations are unknown
2. It is not easy to assume that the two population standard deviations are equal; and
3. The solution for the third scenario is more complex and rigorous and can be applied to other
scenarios
Independent Random Samples - Answers Two (or more) random samples are considered independent if
the process that generates one sample is completely separate from the process that generates the other
sample (e.g., gender: female & male)
x̅1 - x̅2 is a point estimator of u1 - u2 - Answers The values of the sample means x̅1 and x̅2 are computed
from two independent random samples with n1 and n2 observations, respectively
Sampling distribution of x̅1 - x̅2 is assumed to be normally distributed - Answers -A linear combination of
normally distributed random variables is also normally distributed
- If not normal, then by the central limit theorem, the sampling distribution x̅1 - x̅2 is approximately
normal only if both n1 ≥ 30 and n2 ≥ 30
Simple Linear Regression - Answers Projection of future demand based on a past relationship; involves a
single variable.
The correlation coefficient _______ - Answers Captures only a linear relationship
Covariance - Answers Describes the direction of the linear relationship between two variables x and y
Sxy is a _______ - Answers Covariance of two variables in a sample data
Oxy is a _______ - Answers Covariance of two variables in a population data
Correlation Coefficient - Answers Describes both the direction and strength of the relationship between
x and y
Sample Correlation Coefficient - Answers rxy = (Sxy)/(Sx*Sy)
Population Correlation Coefficient - Answers Pxy = (oxy)/(ox*oy)
A correlation of coefficient of 0.12 indicates a _______ - Answers Weak positive relationship
Correlation is NOT causation - Answers -The correlation coefficient captures only a linear relationship
-The correlation coefficient may not be a reliable measure in the presence of outliers
Null Hypothesis (H0) - Answers A statement that you will test. A claim of no difference, meaning that
things are the same as each other. Always specifies a value
Example of a Null Hypothesis - Answers H0: Head = 0.5
Alternative Hypothesis (HA) - Answers A hypothesis opposing the null hypotheses. Never specifies a
value
Example of Alternative Hypothesis - Answers HA: Head ≠ 0.5 or Head < 0.5 or Hero > 0.5
What is the reason to conduct hypothesis tests? - Answers To determine if the sample evidence
contradicts the null hypothesis
If we fail to reject the null hypothesis what does it mean? - Answers It doesn't mean that we accept the
null hypothesis
One-tailed hypothesis test - Answers The alternative hypothesis states that the population parameter is
greater than (right-tailed) or less than (left-tailed) the value specified under the null hypothesis
Example of an One-tailed hypothesis test - Answers H0: u = 50
HA: u > 50 (right-tailed) or u < 50 (left-tailed)
Two-tailed hypothesis test - Answers The alternative hypothesis states that the population parameter is
simply different from the one specified under the null
Example of a Two-tailed hypothesis test - Answers H0: u = 50
HA: u ≠ 50
Type 1 Error - Answers Rejecting the null hypothesis when it's actually true
Type 2 Error - Answers Do not reject the null hypothesis when it's actually false
What is an example of a Type 1 Error - Answers When a jury concludes someone is guilty when in reality
they are innocent
What is an example of a Type 2 Error - Answers When a jury concludes is innocent when in reality they
are guilty
What is the equation for standard error? - Answers s/√ n
What is the equation for T-statistic? - Answers T= (x̅-u)/(s/√ n)
Three scenarios for Two-Sample t-Test - Answers 1. When o1 and o2 are known
2. When o1 and o2 are unknown, but equal
, 3. When o1 and o2 are unknown and unequal
Why do we focus on the third scenario for a Two-Sample t-Test - Answers 1. In general, the population
standard deviations are unknown
2. It is not easy to assume that the two population standard deviations are equal; and
3. The solution for the third scenario is more complex and rigorous and can be applied to other
scenarios
Independent Random Samples - Answers Two (or more) random samples are considered independent if
the process that generates one sample is completely separate from the process that generates the other
sample (e.g., gender: female & male)
x̅1 - x̅2 is a point estimator of u1 - u2 - Answers The values of the sample means x̅1 and x̅2 are computed
from two independent random samples with n1 and n2 observations, respectively
Sampling distribution of x̅1 - x̅2 is assumed to be normally distributed - Answers -A linear combination of
normally distributed random variables is also normally distributed
- If not normal, then by the central limit theorem, the sampling distribution x̅1 - x̅2 is approximately
normal only if both n1 ≥ 30 and n2 ≥ 30
Simple Linear Regression - Answers Projection of future demand based on a past relationship; involves a
single variable.
The correlation coefficient _______ - Answers Captures only a linear relationship
Covariance - Answers Describes the direction of the linear relationship between two variables x and y
Sxy is a _______ - Answers Covariance of two variables in a sample data
Oxy is a _______ - Answers Covariance of two variables in a population data
Correlation Coefficient - Answers Describes both the direction and strength of the relationship between
x and y
Sample Correlation Coefficient - Answers rxy = (Sxy)/(Sx*Sy)
Population Correlation Coefficient - Answers Pxy = (oxy)/(ox*oy)
A correlation of coefficient of 0.12 indicates a _______ - Answers Weak positive relationship
Correlation is NOT causation - Answers -The correlation coefficient captures only a linear relationship
-The correlation coefficient may not be a reliable measure in the presence of outliers
