A 95% confidence interval provides a range of plausible values for the true population parameter. The correct frequentist interpretation is that if the same study were conducted 100 times, 95 of the resulting confidence intervals would be expected to contain the true mean difference in the population.

A Type I error occurs when the null hypothesis is incorrectly rejected. The null hypothesis states there is no difference between the groups. Here, the researchers concluded there was a difference (rejected the null) when in fact no true difference existed. This is the definition of a Type I error (false positive). The probability of making a Type I error is denoted by α.

A Type II error occurs when one fails to reject a null hypothesis that is actually false. In this case, the initial study failed to find a significant effect (did not reject the null hypothesis of no difference) when a true effect existed. This is the definition of a Type II error (false negative). The probability of making a Type II error is denoted by β.

In a skewed distribution, the mean is heavily influenced by extreme values (outliers). The median represents the 50th percentile and is resistant to outliers. Therefore, for skewed data such as income, the median provides a more accurate representation of the central or 'typical' value than the mean.

Power is the ability of a study to detect a true effect (1 - β). The power of a study is primarily influenced by the sample size, effect size, and alpha level. Increasing the sample size is the most common and effective method to increase statistical power, as it reduces the standard error and makes it easier to detect a true difference between groups.

The standard deviation (SD) measures the variability or spread of individual data points within a single sample. The standard error of the mean (SEM) estimates the variability of the means of multiple samples taken from the same population. It quantifies how precisely the sample mean estimates the true population mean and is calculated as SD / √n.

This describes a negatively skewed (left-skewed) distribution. In such a distribution, the outliers are on the lower end. The mode is the most frequent value (the peak), which is 8 hours. The median is less affected by the low-value outliers than the mean. The mean is pulled downward by the low values. Therefore, the relationship is Mean < Median < Mode.

The width of a confidence interval is inversely related to the square root of the sample size. A larger sample size (like in Study B) leads to a smaller standard error of the mean, resulting in a more precise estimate of the true population parameter. This increased precision is reflected by a narrower confidence interval.

While the result is statistically significant (p < 0.05), the absolute difference in survival is only 3%. A critical step in interpreting research is to evaluate whether a statistically significant finding is also clinically meaningful. A small, clinically unimportant difference can become statistically significant if the sample size is very large. Clinicians must decide if a 3% survival benefit justifies the potential costs, side effects, and risks of the new therapy.

The alpha (α) level, or significance level, is the pre-specified probability of committing a Type I error. It is the threshold below which a p-value is considered statistically significant. By convention, α is typically set to 0.05, meaning the researchers accept up to a 5% chance of incorrectly rejecting a true null hypothesis.