Stat 1000 Introduction To Statistics Mock Exam 150 High Yield Mcqs With Detailed Rationales

STAT 1000 INTRODUCTION TO
STATISTICS MOCK EXAM 150
HIGH YIELD MCQS WITH
DETAILED RATIONALES


STAT 1000: Introduction to Statistics Comprehensive
Mock Exam (Questions 1–50)
1. A researcher at a large university in Washington
wants to study the relationship between weekly study
hours and GPA among undergraduate students. She
randomly selects 500 students from the registrar's
database and records their major, age, current GPA,
and average weekly study hours. In this specific study
design, what constitutes the population of interest?
A. The 500 undergraduate students who were randomly
selected and completed the survey.
B. All undergraduate students currently enrolled at
this specific large university.
C. The average GPA and weekly study hours calculated from the
collected sample data.
D. Only the undergraduate students who are majoring in STEM
or statistical disciplines.
Correct Answer: B. All undergraduate students currently
enrolled at this specific large university.
Rationale: The population of interest is the entire group of
individuals that the researcher wants to draw conclusions
about. The 500 randomly selected students represent the
sample used to make inferences about that overall population.

,2. A quality control engineer measures the operational
lifespan of a new batch of LED light bulbs. She records
the lifespans in hours, the ambient room temperature
in Celsius during testing, the manufacturer brand
name, and the binary operational status (Functional
vs. Non-functional). How should these variables be
classified in terms of their data types?
A. Lifespan is nominal, temperature is ordinal, brand name is
ratio, and status is interval.
B. Lifespan is discrete quantitative, temperature is nominal,
brand name is qualitative, and status is continuous
quantitative.
C. Lifespan is continuous quantitative, temperature is
continuous quantitative, brand name is nominal
qualitative, and status is binary qualitative.
D. All four variables are considered continuous quantitative
measurements because they are recorded using numbers or
alphanumeric codes.
Correct Answer: C. Lifespan is continuous quantitative,
temperature is continuous quantitative, brand name is nominal
qualitative, and status is binary qualitative.
Rationale: Lifespan and temperature are quantitative
variables that can take any value within an interval
(continuous). Brand name consists of labels with no natural
ordering (nominal), and status classifies the outcome into
exactly two distinct categories (binary qualitative).
3. Consider a dataset representing the annual salaries
of 11 employees at a small tech startup: $45,000,
$48,000, $50,000, $52,000, $53,000, $55,000,
$58,000, $60,000, $62,000, $65,000, and an
executive salary of $350,000. If the executive's salary
of $350,000 is removed from the dataset, how will the
mean and median of the remaining salaries change?
A. The mean will increase significantly, while the median will
drop to exactly $45,000.

,B. Both the mean and the median will remain entirely
unchanged because they are both highly resistant to extreme
outliers.
C. The mean will decrease substantially, while the
median will experience only a very minor shift.
D. The mean will experience no change at all, but the median
will decrease by more than fifty percent.
Correct Answer: C. The mean will decrease substantially,
while the median will experience only a very minor shift.
Rationale: The mean is highly sensitive to outliers like the
$350,000 salary; removing it shifts the balance point
drastically lower. The median is a resistant measure of center;
removing the maximum value merely shifts the middle
position slightly, keeping it near the center of the dense
cluster.
4. A statistics professor creates a histogram of the
exam scores from a highly challenging midterm. The
resulting distribution displays a very long tail
extending far to the left, with the majority of the scores
clustered tightly on the right side of the graph. What is
the shape of this distribution, and what is the typical
relationship between its measures of central
tendency?
A. The distribution is skewed right; the mean is typically greater
than the median.
B. The distribution is perfectly symmetric; the mean, median,
and mode are all identical.
C. The distribution is skewed left; the mean is typically
less than the median.
D. The distribution is bimodal; the median must be evaluated
using a z-score transformation.
Correct Answer: C. The distribution is skewed left; the mean
is typically less than the median.
Rationale: A distribution with a long tail extending toward the
smaller values on the left is left-skewed (negatively skewed).

, In left-skewed distributions, the low outliers pull the mean
down more forcefully than they affect the median, resulting in
a mean that is smaller than the median.
5. A local health department records the number of
daily influenza cases reported over a 7-day period
during a winter outbreak: 12, 15, 18, 20, 22, 25, and 32.
What are the exact values of the range and the sample
variance (s²) for this 7-day period?
A. The range is 14 cases, and the sample variance is 15.63 cases
squared.
B. The range is 20 cases, and the sample variance is 30.50 cases
squared.
C. The range is 20 cases, and the sample variance is
43.14 cases squared.
D. The range is 32 cases, and the sample variance is 6.57 cases
squared.
Correct Answer: C. The range is 20 cases, and the sample
variance is 43.14 cases squared.
Rationale: The range is Max − Min = 32 − 12 = 20. The sample
mean (x̄) is (12+15+18+20+22+25+32)/7 = 144/7 ≈ 20.57.
Calculating the sum of squared deviations
∑
(
𝑥𝑖
− 𝑥̄
)2
≈258.86
, and dividing by (n - 1) = 6 yields a sample variance of
approximately 43.14.
6. A data analyst computes the five-number summary
for a large set of real estate transactions in a