Why the mean response time is assumed to have a normal distribution?

Question

In this video about hypothesis testing and p-values it is assumed, for some reason (I'm talking about the graph that appears at 3:40), that the mean response time has a normal distribution. Is it because regardless of what the distribution of the time of response is, the mean time has a normal distribution becuase of the Cetral Limit Theorem?

Answer 1

The reason for assuming a normal distribution for the sample mean is that the author is using the Central Limit Theorem (that the distribution of sample mean of a sample of independent identically distributed is approximately normal with mean equal to the population mean and sd equal to the population sd divided by the square root of the sample size). So yes he is relying on the CLT and that 100 is an adequately large sample size.

Answer 2

The standard central limit theorem says that the distribution of the mean of a large sample of iid (independent identically distributed) variables converges approximately to a normal distribution, independent of the underlying distribution of the variable. This means that the mean of a large enough sample follows approximately a normal distribution.

It seems reasonable to assume that the variables are iid, which means that the response time of one rat has no influence on the response time of another rat and that each observation is done with the same circumstances. Furthermore, most textbook call a sample sufficiently large if there are at least 30 observations, in your case there are 100 observations so we may call the sample large.

Note that in this case the distribution of the mean will never really converges to a normal distribution since the mean of response time is always non-negative and the theoretical normal distribution has a domain from minus infinity to plus infinity.