To test the null hypothesis that lengths of stay in two hospitals are equal, which statistical test should be employed?

The appropriate statistical test for comparing the lengths of stay between two hospitals is a t-test for means, specifically designed for assessing whether the means of two independent groups are statistically different from one another. In this context, you are examining two distinct hospitals, each representing a separate group of patients.

Using a t-test for means allows researchers to determine if the average lengths of stay in these two hospitals are significantly different from each other, under the assumption that the data is normally distributed and that the variances of the two groups are similar. This test specifically focuses on the means, which is the parameter of interest in this scenario. The t-test provides a p-value that indicates whether the observed difference in means is likely due to random chance or if it represents a true difference in the hospital lengths of stay.

While other tests may seem relevant, they are not suitable for this specific hypothesis. A one-sample t-test assesses the mean of a single group against a known value, which does not apply when comparing two groups. The two-sample t-test is another term used interchangeably with t-test for means for comparing two independent samples, but "t-test for means" encompasses both the two-sample aspect and the focus on means. A pooled t-test also