Examkin

Question

Difficulty: MediumStatistical Inference and Hypothesis Testing

An epidemiology research group is analyzing data from a large prospective cohort study assessing the risk of chronic kidney disease associated with regular use of a novel non-steroidal anti-inflammatory drug (NSAID). The preliminary report indicates a relative risk of 1.4 for the novel NSAID compared to a standard baseline treatment. The 95% confidence interval for this relative risk is reported as 1.1 to 1.8, and the calculated p-value is 0.03. During peer review, a reviewer suggests that the authors should present a 99% confidence interval instead, to reflect a higher degree of statistical certainty regarding the population parameter. If the authors re-analyze the exact same dataset to generate a 99% confidence interval, which of the following statements best describes how the new interval and the calculated p-value will compare to the preliminary report?

  1. The confidence interval will become wider, and the calculated p-value will remain unchanged.Answer
  2. B
    The confidence interval will become wider, and the calculated p-value will increase.
  3. C
    The confidence interval will become narrower, and the calculated p-value will remain unchanged.
  4. D
    The confidence interval will become narrower, and the calculated p-value will decrease.
  5. E
    The confidence interval will remain the same width, but the calculated p-value will increase.

Answer

The confidence interval will become wider, and the calculated p-value will remain unchanged.
A confidence interval provides a range of values expected to contain the true population parameter with a specific level of certainty. To increase certainty from 95% to 99%, the interval must cast a wider net (using a larger z-score multiplier). Therefore, the 99% confidence interval will always be wider than the 95% confidence interval for the exact same data. On the other hand, the calculated p-value represents the probability of obtaining the observed results assuming the null hypothesis is true. Because the calculated p-value is derived directly from the observed data (sample size, effect size, and variance) and these underlying variables have not changed, the numeric value of the calculated p-value remains exactly 0.03. Note that while the calculated p-value does not change, it is no longer less than the new alpha threshold of 0.01, meaning the result would no longer be considered statistically significant at the 99% confidence level, and the new wider interval would cross the null value of 1.0.

Step-by-Step Solution

1
Analyze the effect of increasing the confidence level on the confidence interval width.
Changing from a 95% confidence level to a 99% confidence level requires using a larger critical value (z-score increases from ~1.96 to ~2.58). This mathematical change makes the resulting interval wider.
A higher confidence level means researchers want to be more certain that the interval contains the true population parameter. To achieve greater certainty, a wider range of values must be included.
2
Determine the relationship between the chosen confidence level and the calculated p-value.
The calculated p-value remains exactly 0.03.
The calculated p-value represents the probability of observing the given results assuming the null hypothesis is true. It is mathematically derived from the sample size, the observed effect size, and the variance in the data. Because the data has not changed, the calculated p-value remains identical, even though the threshold for significance (alpha) changes from 0.05 to 0.01.
3
Synthesize the findings.
The new 99% confidence interval will be wider than the 95% confidence interval, while the calculated p-value will remain unchanged at 0.03.
This correctly pairs the statistical mechanics of confidence interval calculation with the independent nature of the calculated p-value.

Key Concept

Relationship between Confidence Level, Confidence Interval Width, and p-value

Alternative Method

You can visualize this mathematically: CI=estimate±(z×SE)CI = \text{estimate} \pm (z \times SE). For 95% confidence, z≈1.96z \approx 1.96. For 99% confidence, z≈2.58z \approx 2.58. Since 2.58 > 1.96, the interval must be wider. The p-value, however, is calculated purely from the estimate and the SE, neither of which change.
Estimated Time:1m 0s
Rate this question

Topics

Statistical Inference and Hypothesis Testing

More questions from this topic