TEST BANK & SOLUTION MANUAL
FOR ELEMENTARY STATISTICS
14TH EDITION BY MARIO F.
TRIOLA| ALL CHAPTERS| LATEST
Elementary Statistics: Test Bank and Solution Manual
Practice Exam
Instructions: This examination consists of application-based multiple-choice questions.
Each question tests not only recall of statistical concepts but also your ability to apply
this knowledge to realistic scenarios and complex analytical reasoning. Please read each
question and all options carefully before selecting the best answer. The rationale for
each correct answer is provided immediately following the question.
Question 1
A hospital administrator wants to estimate the average length of stay for all patients
admitted to the hospital in the past year. She selects a random sample of 200 patient
records from the hospital's database. The sample has a mean length of stay of 4.8 days
with a standard deviation of 1.2 days. She uses this sample mean to estimate the
population mean. She then constructs a 95% confidence interval for the population
mean and finds it to be (4.63, 4.97). Later, she wants to reduce the width of the
confidence interval by half while maintaining the same level of confidence. Considering
the relationship between sample size, confidence level, and the width of a confidence
interval, which of the following statements most accurately describes the action she
should take and the statistical rationale for it?
A) She should quadruple the sample size to 800, because the width of a confidence
interval is inversely proportional to the square root of the sample size; to halve the
width, the sample size must be increased by a factor of four.
,B) She should double the sample size to 400, because the width of a confidence interval
is inversely proportional to the sample size; to halve the width, the sample size must be
doubled.
C) She should increase the sample size to 400 and reduce the confidence level to 90%,
because both changes will narrow the interval and together they will halve the width.
D) She should keep the sample size the same but use the sample standard deviation
instead of the population standard deviation, because using the sample standard
deviation always produces a narrower interval.
Correct Answer: A
Rationale: Option A is correct because it accurately applies the relationship between
sample size and the width of a confidence interval. The width of a confidence interval for
a population mean is determined by the formula: Width = 2 × (critical value) ×
(standard deviation / √n). Because the width is inversely proportional to the square root
of the sample size (√n), halving the width requires increasing the square root of the
sample size by a factor of 2. This means the sample size must be increased by a factor of
4 (since √4 = 2). To halve the width from the current interval, she would need to
quadruple the sample size from 200 to 800. Option B is incorrect because doubling the
sample size would only reduce the width by a factor of √2 (approximately 1.41), not by
half. Option C is incorrect because while reducing the confidence level would narrow the
interval, combining that change with only doubling the sample size would not achieve a
precise halving of the width, and the question asks for the action specifically to halve the
width while maintaining the same level of confidence. Option D is incorrect because the
sample standard deviation is used when the population standard deviation is unknown;
it does not necessarily produce a narrower interval than the population standard
deviation, and it does not address the sample size issue.
Reference: Triola, Elementary Statistics, Chapter 7: Estimating Parameters and
Determining Sample Sizes.
Question 2
A pharmaceutical company is testing a new drug designed to lower blood pressure. In a
clinical trial, 120 patients with high blood pressure are randomly assigned to either the
treatment group (receiving the new drug) or the control group (receiving a placebo).
After 12 weeks, the mean reduction in systolic blood pressure for the treatment group is
15 mmHg with a standard deviation of 8 mmHg, while the mean reduction for the
control group is 8 mmHg with a standard deviation of 7 mmHg. The company's
statistician conducts a two-sample t-test and obtains a p-value of 0.032. The company's
,leadership is debating whether to proceed with further development of the drug. The
CEO argues that because the p-value is less than 0.05, the drug is proven to be effective
and the company should proceed immediately. The chief scientific officer (CSO) argues
that the p-value alone does not establish clinical significance or practical importance,
and that the company should consider the effect size, confidence interval, and potential
side effects before proceeding. Considering the interpretation of p-values, statistical
significance versus practical significance, and the factors that influence the decision to
proceed with drug development, which of the following statements most accurately
evaluates the two positions?
A) The CEO is correct: a p-value less than 0.05 establishes that the drug is effective with
95% certainty, and the company should proceed immediately with development
because statistical significance is the primary criterion for regulatory approval and
clinical adoption.
B) The CSO is correct: a p-value less than 0.05 indicates that the observed difference is
statistically significant (unlikely to have occurred by chance if the null hypothesis is true),
but it does not establish clinical significance or practical importance; the company
should also consider the effect size (the magnitude of the difference in blood pressure
reduction), the confidence interval for the difference, and potential side effects before
deciding whether to proceed.
C) The CSO is correct, but for a different reason: the p-value is only valid if the sample
size is sufficiently large, and with only 120 patients, the results are not reliable; the
company should increase the sample size to at least 1,000 before making any decisions.
D) The CEO is correct, but the company should also conduct a one-tailed test instead of
a two-tailed test, because a one-tailed test would produce a smaller p-value and provide
stronger evidence of effectiveness.
Correct Answer: B
Rationale: Option B is correct because it accurately describes the interpretation of p-
values and the distinction between statistical significance and practical significance. A p-
value of 0.032 means that if the null hypothesis (no difference between the drug and
placebo) were true, there is a 3.2% probability of observing a difference as large as or
larger than the one observed. This is below the conventional significance level of 0.05,
so the result is statistically significant. However, statistical significance does not
automatically imply clinical or practical significance. The effect size—the magnitude of
the difference in blood pressure reduction (15 mmHg vs. 8 mmHg, a difference of 7
mmHg)—should be evaluated to determine whether the drug's effect is large enough to
be clinically meaningful. The confidence interval for the difference provides a range of
, plausible values for the true effect and indicates the precision of the estimate.
Additionally, potential side effects and the risk-benefit profile must be considered.
Option A is incorrect because statistical significance is not equivalent to proof of
effectiveness; it only indicates that the result is unlikely under the null hypothesis.
Option C is incorrect because the sample size of 120 (60 per group) may be adequate
for detecting a clinically meaningful difference, depending on the power calculation; the
issue is not sample size per se but the distinction between statistical and practical
significance. Option D is incorrect because conducting a one-tailed test after the fact
(post hoc) to obtain a smaller p-value is a form of data dredging or p-hacking, which is
statistically invalid.
Reference: Triola, Elementary Statistics, Chapter 8: Hypothesis Testing.
Question 3
A quality control manager at a manufacturing plant is monitoring the production of a
certain type of electronic component. The plant produces 10,000 components per day.
Historically, the process has produced 2% defective components. The manager wants to
determine whether a new production process has reduced the defect rate. She takes a
random sample of 500 components produced with the new process and finds that 6 are
defective (1.2%). She conducts a hypothesis test for a proportion with the null
hypothesis H₀: p = 0.02 and the alternative hypothesis H₁: p < 0.02. The test statistic is z
= -1.28, and the corresponding p-value is 0.100. The manager is debating whether to
conclude that the new process has reduced the defect rate. The plant supervisor argues
that because the defect rate in the sample (1.2%) is lower than the historical rate (2%),
the new process is clearly better and should be implemented immediately. The manager
argues that the evidence is not strong enough to conclude that the new process has
reduced the defect rate, because the p-value is greater than 0.05. Considering the
interpretation of p-values, the concept of statistical power, and the factors that influence
the decision to reject or fail to reject the null hypothesis, which of the following
statements most accurately evaluates the two positions?
A) The supervisor is correct: the sample defect rate is lower than the historical rate, so
the new process has reduced the defect rate; the p-value is irrelevant because the
sample data clearly show an improvement.
B) The manager is correct: with a p-value of 0.100, which is greater than the
conventional significance level of 0.05, there is insufficient evidence to reject the null
hypothesis; the observed reduction in the sample could be due to random sampling
variability, and failing to reject H₀ does not prove that the new process has not reduced
the defect rate, but it means the evidence is not strong enough to conclude that it has.
FOR ELEMENTARY STATISTICS
14TH EDITION BY MARIO F.
TRIOLA| ALL CHAPTERS| LATEST
Elementary Statistics: Test Bank and Solution Manual
Practice Exam
Instructions: This examination consists of application-based multiple-choice questions.
Each question tests not only recall of statistical concepts but also your ability to apply
this knowledge to realistic scenarios and complex analytical reasoning. Please read each
question and all options carefully before selecting the best answer. The rationale for
each correct answer is provided immediately following the question.
Question 1
A hospital administrator wants to estimate the average length of stay for all patients
admitted to the hospital in the past year. She selects a random sample of 200 patient
records from the hospital's database. The sample has a mean length of stay of 4.8 days
with a standard deviation of 1.2 days. She uses this sample mean to estimate the
population mean. She then constructs a 95% confidence interval for the population
mean and finds it to be (4.63, 4.97). Later, she wants to reduce the width of the
confidence interval by half while maintaining the same level of confidence. Considering
the relationship between sample size, confidence level, and the width of a confidence
interval, which of the following statements most accurately describes the action she
should take and the statistical rationale for it?
A) She should quadruple the sample size to 800, because the width of a confidence
interval is inversely proportional to the square root of the sample size; to halve the
width, the sample size must be increased by a factor of four.
,B) She should double the sample size to 400, because the width of a confidence interval
is inversely proportional to the sample size; to halve the width, the sample size must be
doubled.
C) She should increase the sample size to 400 and reduce the confidence level to 90%,
because both changes will narrow the interval and together they will halve the width.
D) She should keep the sample size the same but use the sample standard deviation
instead of the population standard deviation, because using the sample standard
deviation always produces a narrower interval.
Correct Answer: A
Rationale: Option A is correct because it accurately applies the relationship between
sample size and the width of a confidence interval. The width of a confidence interval for
a population mean is determined by the formula: Width = 2 × (critical value) ×
(standard deviation / √n). Because the width is inversely proportional to the square root
of the sample size (√n), halving the width requires increasing the square root of the
sample size by a factor of 2. This means the sample size must be increased by a factor of
4 (since √4 = 2). To halve the width from the current interval, she would need to
quadruple the sample size from 200 to 800. Option B is incorrect because doubling the
sample size would only reduce the width by a factor of √2 (approximately 1.41), not by
half. Option C is incorrect because while reducing the confidence level would narrow the
interval, combining that change with only doubling the sample size would not achieve a
precise halving of the width, and the question asks for the action specifically to halve the
width while maintaining the same level of confidence. Option D is incorrect because the
sample standard deviation is used when the population standard deviation is unknown;
it does not necessarily produce a narrower interval than the population standard
deviation, and it does not address the sample size issue.
Reference: Triola, Elementary Statistics, Chapter 7: Estimating Parameters and
Determining Sample Sizes.
Question 2
A pharmaceutical company is testing a new drug designed to lower blood pressure. In a
clinical trial, 120 patients with high blood pressure are randomly assigned to either the
treatment group (receiving the new drug) or the control group (receiving a placebo).
After 12 weeks, the mean reduction in systolic blood pressure for the treatment group is
15 mmHg with a standard deviation of 8 mmHg, while the mean reduction for the
control group is 8 mmHg with a standard deviation of 7 mmHg. The company's
statistician conducts a two-sample t-test and obtains a p-value of 0.032. The company's
,leadership is debating whether to proceed with further development of the drug. The
CEO argues that because the p-value is less than 0.05, the drug is proven to be effective
and the company should proceed immediately. The chief scientific officer (CSO) argues
that the p-value alone does not establish clinical significance or practical importance,
and that the company should consider the effect size, confidence interval, and potential
side effects before proceeding. Considering the interpretation of p-values, statistical
significance versus practical significance, and the factors that influence the decision to
proceed with drug development, which of the following statements most accurately
evaluates the two positions?
A) The CEO is correct: a p-value less than 0.05 establishes that the drug is effective with
95% certainty, and the company should proceed immediately with development
because statistical significance is the primary criterion for regulatory approval and
clinical adoption.
B) The CSO is correct: a p-value less than 0.05 indicates that the observed difference is
statistically significant (unlikely to have occurred by chance if the null hypothesis is true),
but it does not establish clinical significance or practical importance; the company
should also consider the effect size (the magnitude of the difference in blood pressure
reduction), the confidence interval for the difference, and potential side effects before
deciding whether to proceed.
C) The CSO is correct, but for a different reason: the p-value is only valid if the sample
size is sufficiently large, and with only 120 patients, the results are not reliable; the
company should increase the sample size to at least 1,000 before making any decisions.
D) The CEO is correct, but the company should also conduct a one-tailed test instead of
a two-tailed test, because a one-tailed test would produce a smaller p-value and provide
stronger evidence of effectiveness.
Correct Answer: B
Rationale: Option B is correct because it accurately describes the interpretation of p-
values and the distinction between statistical significance and practical significance. A p-
value of 0.032 means that if the null hypothesis (no difference between the drug and
placebo) were true, there is a 3.2% probability of observing a difference as large as or
larger than the one observed. This is below the conventional significance level of 0.05,
so the result is statistically significant. However, statistical significance does not
automatically imply clinical or practical significance. The effect size—the magnitude of
the difference in blood pressure reduction (15 mmHg vs. 8 mmHg, a difference of 7
mmHg)—should be evaluated to determine whether the drug's effect is large enough to
be clinically meaningful. The confidence interval for the difference provides a range of
, plausible values for the true effect and indicates the precision of the estimate.
Additionally, potential side effects and the risk-benefit profile must be considered.
Option A is incorrect because statistical significance is not equivalent to proof of
effectiveness; it only indicates that the result is unlikely under the null hypothesis.
Option C is incorrect because the sample size of 120 (60 per group) may be adequate
for detecting a clinically meaningful difference, depending on the power calculation; the
issue is not sample size per se but the distinction between statistical and practical
significance. Option D is incorrect because conducting a one-tailed test after the fact
(post hoc) to obtain a smaller p-value is a form of data dredging or p-hacking, which is
statistically invalid.
Reference: Triola, Elementary Statistics, Chapter 8: Hypothesis Testing.
Question 3
A quality control manager at a manufacturing plant is monitoring the production of a
certain type of electronic component. The plant produces 10,000 components per day.
Historically, the process has produced 2% defective components. The manager wants to
determine whether a new production process has reduced the defect rate. She takes a
random sample of 500 components produced with the new process and finds that 6 are
defective (1.2%). She conducts a hypothesis test for a proportion with the null
hypothesis H₀: p = 0.02 and the alternative hypothesis H₁: p < 0.02. The test statistic is z
= -1.28, and the corresponding p-value is 0.100. The manager is debating whether to
conclude that the new process has reduced the defect rate. The plant supervisor argues
that because the defect rate in the sample (1.2%) is lower than the historical rate (2%),
the new process is clearly better and should be implemented immediately. The manager
argues that the evidence is not strong enough to conclude that the new process has
reduced the defect rate, because the p-value is greater than 0.05. Considering the
interpretation of p-values, the concept of statistical power, and the factors that influence
the decision to reject or fail to reject the null hypothesis, which of the following
statements most accurately evaluates the two positions?
A) The supervisor is correct: the sample defect rate is lower than the historical rate, so
the new process has reduced the defect rate; the p-value is irrelevant because the
sample data clearly show an improvement.
B) The manager is correct: with a p-value of 0.100, which is greater than the
conventional significance level of 0.05, there is insufficient evidence to reject the null
hypothesis; the observed reduction in the sample could be due to random sampling
variability, and failing to reject H₀ does not prove that the new process has not reduced
the defect rate, but it means the evidence is not strong enough to conclude that it has.
