Based on the information below, what would be an example of such a variable?
It is imagined that a researcher collected data from 5000 participants on a variable of interest that is normally distributed. It can be observed that the variable of interest is normally distributed which ranges from -∞ to ∞. And since the range of data is on real line, we can say that the scale of measurement of the variable is ratio, since the sample is taken from 5000 participants of a large population; and since the size of the sample is very large (5000), we can say that the variable is normally distributed.
In defining probability, consider an experiment where you've measured values in two samples, and the means are different. How sure are you that the population means are different as well? There are two possibilities: The populations have different means. The populations have the same mean, and the difference you observed is a coincidence of random sampling.
The p-value is a probability, with a value ranging from zero to one. A p-value is a measure of how much evidence we have against the null hypothesis. In regards to the probability value of .05 being related to the normal curve, the shaded region under a normal curve is equal to the probability of an event occurring. For example, if the entire area under the curve is shaded, then the probability is 1. If nothing is shaded underneath the curve, the probability is 0. .05 means that 5% of the area is shaded, and the probability is equal to .05.