1
ISYE 6414 MIDTERM EXAM 2 – PART 2
DATA ANALYSIS | COMPLETE QUESTIONS,
SOLUTIONS & R CODE | 2026/2027
UPDATED | GEORGIA INSTITUTE OF
TECHNOLOGY
Original practice question bank for exam preparation. These questions are
independently written study materials, not verified copies of Georgia Institute of
Technology exam questions. Results and correctness on an actual exam cannot be
guaranteed.
Introduction
This practice review for ISYE 6414 Midterm Exam 2 – Part 2 focuses on statistical
data analysis, interpretation of model results, and practical R programming skills. It is
designed to help students strengthen their understanding of statistical inference,
regression, hypothesis testing, analysis of variance, model diagnostics, and data-
driven decision-making. Questions emphasize not only selecting an appropriate
statistical method, but also interpreting assumptions, numerical outputs, p-values,
confidence intervals, and practical conclusions.
The R examples use common base-R functions and standard statistical workflows.
Students should practice explaining what the output means rather than memorizing
commands alone. Depending on the semester, instructor, and course materials, the
exact topics and required methods may differ; use this review alongside your official
course notes and assigned exercises.
Core Content Domains
1.
Statistical inference and confidence intervals
2.
3.
Hypothesis testing, p-values, and Type I/II errors
4.
5.
Linear regression and regression diagnostics
,2
6.
7.
Multiple regression and variable selection
8.
9.
Analysis of variance (ANOVA)
10.
11.
Correlation and covariance
12.
13.
Probability distributions and sampling
14.
15.
Model assumptions and residual analysis
16.
17.
Statistical computing and R programming
18.
19.
Interpretation of statistical output and data-analysis decisions
20.
QUESTIONS 1–100
Domain 1: Statistical Inference and
Confidence Intervals
Question 1
A researcher calculates a 95% confidence interval for a population mean of (42.1,
48.7). Which interpretation is most appropriate?
,3
A. There is a 95% probability that the fixed population mean changes within this
interval.
B. The procedure used to construct intervals would capture the true population mean
in approximately 95% of repeated samples.
C. Exactly 95% of individual observations fall within the interval.
D. The sample mean is correct 95% of the time.
Rationale: A confidence interval is produced by a procedure with a long-run coverage
rate. If the sampling and interval assumptions hold, approximately 95% of intervals
constructed this way would contain the fixed population parameter. Option A
incorrectly assigns a frequentist probability to a fixed parameter after the interval has
been calculated. Option C confuses a confidence interval for a mean with an interval
describing individual observations. Option D misinterprets confidence as the
probability that the sample mean is correct.
Question 2
A sample of 64 observations has a mean of 100 and a known population standard
deviation of 16. What is the standard error of the sample mean?
A. 16
B. 4
C. 2
D. 8
Rationale: The standard error is \(\sigma/\sqrt{n}\). Here, \(16/\sqrt{64}=16/8=2\).
Option A gives the population standard deviation, not the standard error. Option B
divides by 4 rather than by the square root of 64, which is 8. Option D divides the
standard deviation by 2, which does not use the correct sample-size formula.
Question 3
Which change generally makes a confidence interval for a population mean narrower,
assuming the other conditions remain unchanged?
A. Increasing the sample size
B. Increasing the confidence level
C. Increasing the standard deviation
D. Increasing the standard error
, 4
Rationale: Increasing sample size usually reduces the standard error because it is
proportional to \(1/\sqrt{n}\). This narrows the interval. Option B increases the critical
value and generally widens the interval. Option C increases variability and generally
widens the interval. Option D directly increases the margin of error, making the
interval wider.
Question 4
A sample of 25 observations has a sample mean of 72 and a sample standard
deviation of 10. Assuming an appropriate random sample from a normally distributed
population, which distribution should be used to construct a confidence interval for
the population mean?
A. Standard normal distribution with known population standard deviation
B. Student's t-distribution with 24 degrees of freedom
C. Chi-square distribution with 25 degrees of freedom
D. F-distribution with 24 and 25 degrees of freedom
Rationale: When the population standard deviation is unknown and the sample
standard deviation is used, the one-sample mean interval uses Student's t-distribution.
The degrees of freedom are \(n-1=24\). Option A assumes the population standard
deviation is known. Option C is commonly used for inference about a normal
population variance. Option D is associated with variance-ratio procedures and certain
ANOVA tests.
Question 5
A 95% confidence interval for a population mean difference is (−1.4, 3.2). At the 5%
significance level, what does this imply for a corresponding two-sided test of a zero
difference?
A. Reject the null hypothesis because the interval contains positive values.
B. Reject the null hypothesis because the interval contains negative values.
C. Fail to reject the null hypothesis because zero is inside the interval.
D. Prove that the two population means are equal.
Rationale: A two-sided test at significance level 0.05 is generally consistent with a
95% confidence interval. Since zero lies in the interval, the data do not provide
sufficient evidence to reject a zero difference at that level. Options A and B
incorrectly treat the presence of positive or negative values as sufficient for rejection.
Option D overstates the result: failure to reject does not establish equality.
Question 6
ISYE 6414 MIDTERM EXAM 2 – PART 2
DATA ANALYSIS | COMPLETE QUESTIONS,
SOLUTIONS & R CODE | 2026/2027
UPDATED | GEORGIA INSTITUTE OF
TECHNOLOGY
Original practice question bank for exam preparation. These questions are
independently written study materials, not verified copies of Georgia Institute of
Technology exam questions. Results and correctness on an actual exam cannot be
guaranteed.
Introduction
This practice review for ISYE 6414 Midterm Exam 2 – Part 2 focuses on statistical
data analysis, interpretation of model results, and practical R programming skills. It is
designed to help students strengthen their understanding of statistical inference,
regression, hypothesis testing, analysis of variance, model diagnostics, and data-
driven decision-making. Questions emphasize not only selecting an appropriate
statistical method, but also interpreting assumptions, numerical outputs, p-values,
confidence intervals, and practical conclusions.
The R examples use common base-R functions and standard statistical workflows.
Students should practice explaining what the output means rather than memorizing
commands alone. Depending on the semester, instructor, and course materials, the
exact topics and required methods may differ; use this review alongside your official
course notes and assigned exercises.
Core Content Domains
1.
Statistical inference and confidence intervals
2.
3.
Hypothesis testing, p-values, and Type I/II errors
4.
5.
Linear regression and regression diagnostics
,2
6.
7.
Multiple regression and variable selection
8.
9.
Analysis of variance (ANOVA)
10.
11.
Correlation and covariance
12.
13.
Probability distributions and sampling
14.
15.
Model assumptions and residual analysis
16.
17.
Statistical computing and R programming
18.
19.
Interpretation of statistical output and data-analysis decisions
20.
QUESTIONS 1–100
Domain 1: Statistical Inference and
Confidence Intervals
Question 1
A researcher calculates a 95% confidence interval for a population mean of (42.1,
48.7). Which interpretation is most appropriate?
,3
A. There is a 95% probability that the fixed population mean changes within this
interval.
B. The procedure used to construct intervals would capture the true population mean
in approximately 95% of repeated samples.
C. Exactly 95% of individual observations fall within the interval.
D. The sample mean is correct 95% of the time.
Rationale: A confidence interval is produced by a procedure with a long-run coverage
rate. If the sampling and interval assumptions hold, approximately 95% of intervals
constructed this way would contain the fixed population parameter. Option A
incorrectly assigns a frequentist probability to a fixed parameter after the interval has
been calculated. Option C confuses a confidence interval for a mean with an interval
describing individual observations. Option D misinterprets confidence as the
probability that the sample mean is correct.
Question 2
A sample of 64 observations has a mean of 100 and a known population standard
deviation of 16. What is the standard error of the sample mean?
A. 16
B. 4
C. 2
D. 8
Rationale: The standard error is \(\sigma/\sqrt{n}\). Here, \(16/\sqrt{64}=16/8=2\).
Option A gives the population standard deviation, not the standard error. Option B
divides by 4 rather than by the square root of 64, which is 8. Option D divides the
standard deviation by 2, which does not use the correct sample-size formula.
Question 3
Which change generally makes a confidence interval for a population mean narrower,
assuming the other conditions remain unchanged?
A. Increasing the sample size
B. Increasing the confidence level
C. Increasing the standard deviation
D. Increasing the standard error
, 4
Rationale: Increasing sample size usually reduces the standard error because it is
proportional to \(1/\sqrt{n}\). This narrows the interval. Option B increases the critical
value and generally widens the interval. Option C increases variability and generally
widens the interval. Option D directly increases the margin of error, making the
interval wider.
Question 4
A sample of 25 observations has a sample mean of 72 and a sample standard
deviation of 10. Assuming an appropriate random sample from a normally distributed
population, which distribution should be used to construct a confidence interval for
the population mean?
A. Standard normal distribution with known population standard deviation
B. Student's t-distribution with 24 degrees of freedom
C. Chi-square distribution with 25 degrees of freedom
D. F-distribution with 24 and 25 degrees of freedom
Rationale: When the population standard deviation is unknown and the sample
standard deviation is used, the one-sample mean interval uses Student's t-distribution.
The degrees of freedom are \(n-1=24\). Option A assumes the population standard
deviation is known. Option C is commonly used for inference about a normal
population variance. Option D is associated with variance-ratio procedures and certain
ANOVA tests.
Question 5
A 95% confidence interval for a population mean difference is (−1.4, 3.2). At the 5%
significance level, what does this imply for a corresponding two-sided test of a zero
difference?
A. Reject the null hypothesis because the interval contains positive values.
B. Reject the null hypothesis because the interval contains negative values.
C. Fail to reject the null hypothesis because zero is inside the interval.
D. Prove that the two population means are equal.
Rationale: A two-sided test at significance level 0.05 is generally consistent with a
95% confidence interval. Since zero lies in the interval, the data do not provide
sufficient evidence to reject a zero difference at that level. Options A and B
incorrectly treat the presence of positive or negative values as sufficient for rejection.
Option D overstates the result: failure to reject does not establish equality.
Question 6
