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Difficulty: MediumStatistical Inference and Hypothesis Testing

Pulmonologists at a tertiary care center are analyzing data from a recent multi-center clinical trial. The trial investigated whether adding a novel interleukin-5 inhibitor to standard therapy improves lung function in patients with severe eosinophilic asthma. The investigators measured the change in forced expiratory volume in 1 second (FEV1FEV_1) from baseline to week 24. Results demonstrate that patients receiving the novel biologic had a mean FEV1FEV_1 improvement that was 150 mL150 \text{ mL} greater than those receiving standard therapy alone. The 95% confidence interval for this mean difference spans from 40 mL40 \text{ mL} to 260 mL260 \text{ mL}. Which of the following is the most appropriate statistical interpretation of these data?

  1. The p-value for the mean difference is less than 0.05.Answer
  2. B
    Constructing a 99% confidence interval from these data would yield a narrower range than the reported interval.
  3. C
    The trial lacks sufficient statistical power, indicating a high probability of a Type II error.
  4. D
    There is a 95% probability that the true population mean difference is exactly 150 mL.
  5. E
    The null hypothesis was successfully rejected specifically because the confidence interval does not include 1.0.

Answer

The p-value for the mean difference is less than 0.05.
The study reports a 95% confidence interval for a mean difference that ranges from 40 mL40 \text{ mL} to 260 mL260 \text{ mL}. For a difference in continuous means, the null hypothesis posits that there is no difference between the groups, meaning the null value is 0. Because the entire 95% confidence interval excludes 0, we can reject the null hypothesis at the α=0.05\alpha = 0.05 significance level. This mathematically guarantees that the corresponding p-value for this finding is less than 0.05.

Step-by-Step Solution

1
Identify the statistical parameter being estimated in the study.
The study is evaluating a difference in means (FEV1FEV_1 improvement between two groups).
Identifying the parameter is necessary to determine the appropriate null value.
2
Determine the correct null value for a mean difference.
The null value for a difference between two group means is 0 (indicating no difference).
Confidence intervals are compared against the null value to assess statistical significance.
3
Evaluate the reported confidence interval relative to the null value.
The 95% confidence interval (40 mL40 \text{ mL} to 260 mL260 \text{ mL}) is entirely above 0.
Because the 95% confidence interval excludes the null value, the result is statistically significant at the α=0.05\alpha = 0.05 level, which mathematically guarantees a corresponding p-value of less than 0.05.

Key Concept

The relationship between confidence intervals and p-values: a 95% confidence interval that excludes the null value corresponds to a statistically significant p-value of less than 0.05.
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Topics

Statistical Inference and Hypothesis Testing

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