UMICH STATS 250 - FINAL EXAM QUESTIONS AND
ANSWERS 2026
One sample and a categorical response variable - What is the assumption? - Answers -
The sample is large enough; at least ten successes and ten failures
Two independent samples and a quantitative response variable - what is the
assumption? - Answers -Each of the samples was drawn from a population of
responses that are normally distributed
Two dependent samples and a quantitative response variable - what is the assumption?
- Answers -The sample of differences was drawn from a population of differences that
are normally distributed
A t-test statistic measures how much the (a)____deviates from the hypothesized
(b)____, in standard error units - Answers -a. sample mean
b. population mean
The Central Limit Theorem states that as the size of the (a)____ increases, the
distribution of the (b)____ will increasingly resemble a normal distribution, regardless of
the shape of the population's distribution. - Answers -a. sample of quantitative
observations
b. sample mean
The goal of a confidence interval for one mean is to provide a range of reasonable
values for the (a)____. To create this range of values, we center the interval on the
(b)____ and use the (c)___ to help construct a margin of error that provides a measure
of the precision of the estimate. - Answers -a. population mean
b. sample mean
c. sample standard deviation
A QQ plot shows if the (a)____ is normally distributed. If the points roughly follow the
identity line, we can assume that the sample was drawn from a (b)____ that is normally
distributed, which is a key assumption that must be made to perform inferences for
poplation means. - Answers -a. sample of quantitative observations
b. population of quantitative observations
Given this confidence interval, is the statement below accurate?
There is a 95% chance that the true difference in RDI levels between men and women
is contained in the interval above. - Answers -incorrect
, Continuing from above, in repeated random samples, we expect approximately 95% of
all differences in sample means xbar1 - xbar2 will fall within the observed bounds of the
interval above. - Answers -incorrect
We can be 95% confident that the true difference in mean RDI levels between men and
women with traumatic brain injuries is contained within the bounds of the interval above.
- Answers -correct
If you want the hypothetical study to replicate the observed effect size of the initial study
what needs to happen? - Answers -The sample means and standard deviations need
to remain the same
If you are replicating a study and would like to produce a p-value that is larger than the
one from the initial study what needs to happen? - Answers -The standard deviation
would change while the sample size and sample means would remain the same
If you are replicating a study and would like to produce a p-value that is smaller than the
one from the initial study? - Answers -The standard deviation remains the same.
However, either the sample size or sample means would change.
What hypothesis is used to calculate a population slope? - Answers -T-test
How do you calculate the degrees of freedom for a linear regression model?
(Distribution form) - Answers -T(n-2)
What are the three assumptions of a linear regression model? - Answers -1. Linearity
2. Normality
3. Constant Variability
What type of plot or graph is used to determine normality? - Answers -QQ plot or a
histogram
What type of plot is used to evaluate variance and linearity? - Answers -Residuals vs
Fitted Plot
The (a)____ and (b)____ should align with the confidence interval conclusions -
Answers -a. Test statistic
b. P-value
How do you interpret a t-test statistic? - Answers -Our observed sample slope of ____
falls ____ standard errors (above or below) the hypothesized population level slope of
zero
What should you never see in a residuals vs. fitted plot? - Answers -You should never
see a dicer able pattern or curve because that means linearity and variance are violated
ANSWERS 2026
One sample and a categorical response variable - What is the assumption? - Answers -
The sample is large enough; at least ten successes and ten failures
Two independent samples and a quantitative response variable - what is the
assumption? - Answers -Each of the samples was drawn from a population of
responses that are normally distributed
Two dependent samples and a quantitative response variable - what is the assumption?
- Answers -The sample of differences was drawn from a population of differences that
are normally distributed
A t-test statistic measures how much the (a)____deviates from the hypothesized
(b)____, in standard error units - Answers -a. sample mean
b. population mean
The Central Limit Theorem states that as the size of the (a)____ increases, the
distribution of the (b)____ will increasingly resemble a normal distribution, regardless of
the shape of the population's distribution. - Answers -a. sample of quantitative
observations
b. sample mean
The goal of a confidence interval for one mean is to provide a range of reasonable
values for the (a)____. To create this range of values, we center the interval on the
(b)____ and use the (c)___ to help construct a margin of error that provides a measure
of the precision of the estimate. - Answers -a. population mean
b. sample mean
c. sample standard deviation
A QQ plot shows if the (a)____ is normally distributed. If the points roughly follow the
identity line, we can assume that the sample was drawn from a (b)____ that is normally
distributed, which is a key assumption that must be made to perform inferences for
poplation means. - Answers -a. sample of quantitative observations
b. population of quantitative observations
Given this confidence interval, is the statement below accurate?
There is a 95% chance that the true difference in RDI levels between men and women
is contained in the interval above. - Answers -incorrect
, Continuing from above, in repeated random samples, we expect approximately 95% of
all differences in sample means xbar1 - xbar2 will fall within the observed bounds of the
interval above. - Answers -incorrect
We can be 95% confident that the true difference in mean RDI levels between men and
women with traumatic brain injuries is contained within the bounds of the interval above.
- Answers -correct
If you want the hypothetical study to replicate the observed effect size of the initial study
what needs to happen? - Answers -The sample means and standard deviations need
to remain the same
If you are replicating a study and would like to produce a p-value that is larger than the
one from the initial study what needs to happen? - Answers -The standard deviation
would change while the sample size and sample means would remain the same
If you are replicating a study and would like to produce a p-value that is smaller than the
one from the initial study? - Answers -The standard deviation remains the same.
However, either the sample size or sample means would change.
What hypothesis is used to calculate a population slope? - Answers -T-test
How do you calculate the degrees of freedom for a linear regression model?
(Distribution form) - Answers -T(n-2)
What are the three assumptions of a linear regression model? - Answers -1. Linearity
2. Normality
3. Constant Variability
What type of plot or graph is used to determine normality? - Answers -QQ plot or a
histogram
What type of plot is used to evaluate variance and linearity? - Answers -Residuals vs
Fitted Plot
The (a)____ and (b)____ should align with the confidence interval conclusions -
Answers -a. Test statistic
b. P-value
How do you interpret a t-test statistic? - Answers -Our observed sample slope of ____
falls ____ standard errors (above or below) the hypothesized population level slope of
zero
What should you never see in a residuals vs. fitted plot? - Answers -You should never
see a dicer able pattern or curve because that means linearity and variance are violated
