# This means that the null hypothesis would be written as

The Brinell hardness scale is one of several definitions used in the field of materials science to quantify the hardness of a piece of metal. The Brinell hardness measurement of a certain type of rebar used for reinforcing concrete and masonry structures was assumed to be normally distributed with a standard deviation of 10 kilograms of force per square millimeter. Using a random sample of *n* = 25 bars, an engineer is interested in performing the following hypothesis test:

## the null hypothesis is rejected when it is true b.

### the null hypothesis is not rejected when it is false c.

Generally speaking, one-tailed tests are often reserved for situations where a clear directional outcome is anticipated or where changes in only one direction are relevant to the goals of the study. Examples of the latter are perhaps more often encountered in industry settings, such as testing a drug for the alleviation of symptoms. In this case, there is no reason to be interested in proving that a drug worsens symptoms, only that it improves them. In such situations, a one-tailed test may be suitable. Another example would be tracing the population of an endangered species over time, where the anticipated direction is clear and where the cost of being too conservative in the interpretation of data could lead to extinction. Notably, for the field of experimental biology, these circumstances rarely, if ever, arise. In part for this reason, two-tailed tests are more common and further serve to dispel any suggestion that one has manipulated the test to obtain a desired outcome.

### the research hypothesis is not rejected when it is false722-1

Also, just to reinforce a point raised earlier, greater variance in the sample data will lead to higher -values because of the effect of sample variance on the SEDM. This will make it more difficult to detect differences between sample means using the -test. Even without any technical explanation, this makes intuitive sense given that greater scatter in the data will create a level of background noise that could obscure potential differences. This is particularly true if the differences in means are small relative to the amount of scatter. This can be compensated for to some extent by increasing the sample size. This, however, may not be practical in some cases, and there can be downsides associated with accumulating data solely for the purpose of obtaining low -values (see ).