MATH 225N WEEK 7 LAB ASSIGNMENT SUMMER 2026/2027 |
Complete Solution Guide | Statistical Reasoning for Health
Sciences | Chamberlain University | Pass Guaranteed - A+
Graded
[Section 1: Hypothesis Testing Fundamentals (Questions 1-10)]
Question 1
A nurse researcher wants to test whether a new wound care protocol reduces healing
time compared to the standard protocol. The null hypothesis (H₀) states that there is no
difference in mean healing time between the new and standard protocols. What is the
correct symbolic representation of the null hypothesis for the two populations?
A. H₀: μ₁ > μ₂ [CORRECT]
B. H₀: μ₁ ≠ μ₂
C. H₀: μ₁ = μ₂ [CORRECT]
D. H₀: μ₁ < μ₂
Correct Answer: C
Rationale: The null hypothesis always represents "no effect" or "no difference,"
symbolized as H₀: μ₁ = μ₂ (the population means are equal). Option A and D represent
directional alternative hypotheses, while B represents a two-tailed alternative
hypothesis. In nursing research, the null hypothesis serves as the default position that
the intervention has no effect, which we seek evidence to reject. APA reporting tip:
Always state H₀ symbolically and in words.
,Question 2
A clinical trial tests whether a new antihypertensive medication lowers systolic blood
pressure more than placebo. The researcher predicts the medication will produce lower
BP readings. What type of hypothesis test should be used?
A. Two-tailed test because the researcher is unsure of the direction
B. One-tailed test because the hypothesis predicts a specific directional effect
[CORRECT]
C. Two-tailed test because all clinical research requires two-tailed testing
D. One-tailed test because it always produces a more significant p-value
Correct Answer: B
Rationale: A one-tailed (directional) test is appropriate when the research hypothesis
predicts a specific direction of effect—in this case, that the medication will lower BP
(not raise it). Option A is incorrect because the researcher has a directional prediction.
Option C is false; while two-tailed tests are common, directional hypotheses warrant
one-tailed tests. Option D misrepresents the purpose; one-tailed tests are not chosen to
obtain significance but because the research question is directional.
Question 3
In a study comparing fall rates before and after implementing a new safety protocol, the
researcher concludes the protocol is effective when it actually is not. What type of error
has occurred?
A. Type II error (false negative)
B. Type I error (false positive) [CORRECT]
C. Type III error (wrong model specification)
D. No error; this is correct statistical decision-making
,Correct Answer: B
Rationale: A Type I error (false positive, α risk) occurs when we reject a true null
hypothesis—concluding there is an effect when none exists. In this clinical scenario, the
researcher falsely concluded the safety protocol works. The α level (typically 0.05)
controls this risk. A Type II error (A) would be failing to detect a truly effective protocol.
Type III error (C) refers to correctly rejecting H₀ but for the wrong reason. In patient
safety research, Type I errors can lead to implementing costly, ineffective interventions.
Question 4
A nursing student interprets a p-value of 0.032 from a t-test comparing pain scores
between two analgesic groups. Which statement is the CORRECT interpretation?
A. There is a 3.2% probability that the null hypothesis is true
B. There is a 3.2% probability of obtaining the observed data or more extreme results if
the null hypothesis is true [CORRECT]
C. There is a 96.8% probability that the alternative hypothesis is true
D. There is a 3.2% probability that the observed difference is due to chance alone
Correct Answer: B
Rationale: The p-value represents the probability of observing the sample data (or more
extreme) assuming H₀ is true—not the probability that H₀ is true (A) or that Hₐ is true (C).
Option D is a common misconception; the p-value does not measure the probability that
results are "due to chance." At α = 0.05, p = 0.032 < 0.05, so we reject H₀ and conclude a
statistically significant difference exists. APA reporting: t(df) = x.xx, p = .032.
Question 5
, A researcher sets α = 0.05 for a study comparing ICU length of stay across three nursing
shift assignments. What does this significance level represent?
A. The probability of correctly rejecting a false null hypothesis (power)
B. The maximum probability of committing a Type I error the researcher is willing to
accept [CORRECT]
C. The probability that the study results are clinically meaningful
D. The probability of obtaining a significant result when the effect size is large
Correct Answer: B
Rationale: The significance level (α = 0.05) is the threshold for the maximum acceptable
probability of a Type I error—rejecting a true null hypothesis. It does not represent power
(A), clinical significance (C), or a guarantee of significance with large effects (D). In
healthcare research, α = 0.05 is standard because it balances the risk of false positives
against the need to detect true effects. Setting α lower (e.g., 0.01) reduces Type I error
risk but increases Type II error risk.
Question 6
In a study testing whether nurse-patient ratios affect patient satisfaction scores, the
researcher obtains a test statistic of z = 2.15 with a corresponding p-value of 0.0316. At
α = 0.05, what is the correct statistical decision?
A. Fail to reject H₀ because 2.15 < critical value of 1.96
B. Reject H₀ because p = 0.0316 < 0.05 [CORRECT]
C. Fail to reject H₀ because the effect may not be clinically significant
D. Reject H₀ because z = 2.15 indicates a large effect size
Correct Answer: B
Rationale: The decision rule is: if p ≤ α, reject H₀. Here, p = 0.0316 < 0.05, so we reject H₀
and conclude a statistically significant relationship exists. Option A is incorrect because
Complete Solution Guide | Statistical Reasoning for Health
Sciences | Chamberlain University | Pass Guaranteed - A+
Graded
[Section 1: Hypothesis Testing Fundamentals (Questions 1-10)]
Question 1
A nurse researcher wants to test whether a new wound care protocol reduces healing
time compared to the standard protocol. The null hypothesis (H₀) states that there is no
difference in mean healing time between the new and standard protocols. What is the
correct symbolic representation of the null hypothesis for the two populations?
A. H₀: μ₁ > μ₂ [CORRECT]
B. H₀: μ₁ ≠ μ₂
C. H₀: μ₁ = μ₂ [CORRECT]
D. H₀: μ₁ < μ₂
Correct Answer: C
Rationale: The null hypothesis always represents "no effect" or "no difference,"
symbolized as H₀: μ₁ = μ₂ (the population means are equal). Option A and D represent
directional alternative hypotheses, while B represents a two-tailed alternative
hypothesis. In nursing research, the null hypothesis serves as the default position that
the intervention has no effect, which we seek evidence to reject. APA reporting tip:
Always state H₀ symbolically and in words.
,Question 2
A clinical trial tests whether a new antihypertensive medication lowers systolic blood
pressure more than placebo. The researcher predicts the medication will produce lower
BP readings. What type of hypothesis test should be used?
A. Two-tailed test because the researcher is unsure of the direction
B. One-tailed test because the hypothesis predicts a specific directional effect
[CORRECT]
C. Two-tailed test because all clinical research requires two-tailed testing
D. One-tailed test because it always produces a more significant p-value
Correct Answer: B
Rationale: A one-tailed (directional) test is appropriate when the research hypothesis
predicts a specific direction of effect—in this case, that the medication will lower BP
(not raise it). Option A is incorrect because the researcher has a directional prediction.
Option C is false; while two-tailed tests are common, directional hypotheses warrant
one-tailed tests. Option D misrepresents the purpose; one-tailed tests are not chosen to
obtain significance but because the research question is directional.
Question 3
In a study comparing fall rates before and after implementing a new safety protocol, the
researcher concludes the protocol is effective when it actually is not. What type of error
has occurred?
A. Type II error (false negative)
B. Type I error (false positive) [CORRECT]
C. Type III error (wrong model specification)
D. No error; this is correct statistical decision-making
,Correct Answer: B
Rationale: A Type I error (false positive, α risk) occurs when we reject a true null
hypothesis—concluding there is an effect when none exists. In this clinical scenario, the
researcher falsely concluded the safety protocol works. The α level (typically 0.05)
controls this risk. A Type II error (A) would be failing to detect a truly effective protocol.
Type III error (C) refers to correctly rejecting H₀ but for the wrong reason. In patient
safety research, Type I errors can lead to implementing costly, ineffective interventions.
Question 4
A nursing student interprets a p-value of 0.032 from a t-test comparing pain scores
between two analgesic groups. Which statement is the CORRECT interpretation?
A. There is a 3.2% probability that the null hypothesis is true
B. There is a 3.2% probability of obtaining the observed data or more extreme results if
the null hypothesis is true [CORRECT]
C. There is a 96.8% probability that the alternative hypothesis is true
D. There is a 3.2% probability that the observed difference is due to chance alone
Correct Answer: B
Rationale: The p-value represents the probability of observing the sample data (or more
extreme) assuming H₀ is true—not the probability that H₀ is true (A) or that Hₐ is true (C).
Option D is a common misconception; the p-value does not measure the probability that
results are "due to chance." At α = 0.05, p = 0.032 < 0.05, so we reject H₀ and conclude a
statistically significant difference exists. APA reporting: t(df) = x.xx, p = .032.
Question 5
, A researcher sets α = 0.05 for a study comparing ICU length of stay across three nursing
shift assignments. What does this significance level represent?
A. The probability of correctly rejecting a false null hypothesis (power)
B. The maximum probability of committing a Type I error the researcher is willing to
accept [CORRECT]
C. The probability that the study results are clinically meaningful
D. The probability of obtaining a significant result when the effect size is large
Correct Answer: B
Rationale: The significance level (α = 0.05) is the threshold for the maximum acceptable
probability of a Type I error—rejecting a true null hypothesis. It does not represent power
(A), clinical significance (C), or a guarantee of significance with large effects (D). In
healthcare research, α = 0.05 is standard because it balances the risk of false positives
against the need to detect true effects. Setting α lower (e.g., 0.01) reduces Type I error
risk but increases Type II error risk.
Question 6
In a study testing whether nurse-patient ratios affect patient satisfaction scores, the
researcher obtains a test statistic of z = 2.15 with a corresponding p-value of 0.0316. At
α = 0.05, what is the correct statistical decision?
A. Fail to reject H₀ because 2.15 < critical value of 1.96
B. Reject H₀ because p = 0.0316 < 0.05 [CORRECT]
C. Fail to reject H₀ because the effect may not be clinically significant
D. Reject H₀ because z = 2.15 indicates a large effect size
Correct Answer: B
Rationale: The decision rule is: if p ≤ α, reject H₀. Here, p = 0.0316 < 0.05, so we reject H₀
and conclude a statistically significant relationship exists. Option A is incorrect because
