Manufacturer A supplies 9 units for lifetime test. We are concerned with the lifetime of the component and want to choose the manufacturer that affords the longer lifetime.
Two manufacturers, denoted by A and B, are suppliers for a component. To understand this, consider a well-posted example that is originally given in a textbook of Roberts. In my opinion, the two-sample t-test can be misleading it may not provide a valid solution to practical problems. Therefore, abandoning the NHSTP means abandoning the two-sample t-test. The t-test, especially the two-sample t-test, is the most commonly used NHSTP. But when the design gets more complicates (more-factorial designs, paired or longitudinal designs, designs wirth nested and/or random effects) the calculation of a simple group mean becomes cumbersome or even impossible, but yet the effects are estimated and the precision of these estimates can be given. In simpler designs such group means and their SEs can be easily calculated and so they are presented. Often, the estimates of the "group means" are rather irrelevant, and so are their SEs. This estimate like the difference, the treatment effect, does not have a SD there is only a SE. The really relevant estimate is the difference between the groups, and for this estimate the SE could/should* be (but is typically not!) provided.
Therefor it makes only very limited sense to present the precision of the mean BMI for the two groups. The central question is about the DIFFERENCE of the BMI between these groups. The central question is *NOT* the BMI of the controls and *NOT* the BMI of the treated. "does a high omega-6-fatty acid diet reduce the BMI?"). A typical research question is of the tyle like "does my treatment have an effect on the BMI?" (e.g.
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