We recognize that we have two sample means, one from each set of data, and thus we have two random variables coming from two unknown distributions. Our question has not changed: Do these two samples come from the same population distribution? To approach this problem we create a new random variable.
Now we are interested in whether or not two samples have the same mean. In both cases that was the question: what is the probability that the mean (or proportion) from our sample data came from a population distribution with the hypothesized value we are interested in?
DIFFERENCE BETWEEN TWO MEAN HYPOTHESIS TEST CALCULATOR HOW TO
This provided us with the solution to our question of how to measure the probability that a sample mean came from a distribution with a particular hypothesized value of the mean or proportion. Our Z and t statistics came from this theorem. The Central Limit Theorem gave us the answer: the normal distribution. It was important for us to know the distribution that these random variables came from. This made our sample parameters, the sample means and sample proportions, into random variables. We recognized that a sample mean came from a distribution of sample means, and sample proportions came from the sampling distribution of sample proportions. When we developed the hypothesis test for the mean and proportions we began with the Central Limit Theorem. The degrees of freedom formula we will see later was developed by Aspin-Welch.
The test comparing two independent population means with unknown and possibly unequal population standard deviations is called the Aspin-Welch t-test. The test statistic will have to account for this fact. Very different means can occur by chance if there is great variation among the individual samples. Is the night shift less productive than the day shift, are the rates of return from fixed asset investments different from those from common stock investments, and so on? An observed difference between two sample means depends on both the means and the sample standard deviations. The comparison of two independent population means is very common and provides a way to test the hypothesis that the two groups differ from each other.
0 kommentar(er)
