So, to overcome this issue, we will look into the second option to collect a small sample of salaries of data analysts and take their average as India average. This is the inferential statistics where we make an inference from a sample about the population. It is a measure of the chance of occurrence of a phenomenon. We will now discuss some terms which are very important in probability:. Conditional probability is the probability of a particular event Y, given a certain condition which has already occurred , i.
Then conditional probability, P Y X is defined as,. The mathematical function describing the randomness of a random variable is called probability distribution. It is a depiction of all possible outcomes of a random variable and their associated probabilities. Probability distribution of statistics of a large number of samples selected from the population is called sampling distribution.
When we increase the size of sample, sample mean becomes more normally distributed around population mean. The variability of the sample decreases as we increase sample size. CLT tells that when we increase the sample size, the distribution of sample means becomes normally distributed as the sample, whatever be the population distribution shape.
This theorem is particularly true when we have a sample of size greater than The conclusion is that if we take a greater number of samples and particularly of large sizes, the distribution of sample means in a graph will look like to follow the normal distribution. In the above graph we can see that when we increase the value of n i. Confidence Interval is an interval of reasonable values for our parameters. Confidence intervals are used to give an interval estimation for our parameter of interest.
Hypothesis testing is a part of statistics in which we make assumptions about the population parameter. So, hypothesis testing mentions a proper procedure by analysing a random sample of the population to accept or reject the assumption. The process to determine whether to reject a null hypothesis or to fail to reject the null hypothesis, based on sample data is called hypothesis testing.
It consists of four steps:. If the value of t-stat is less than the significance level we will reject the null hypothesis, otherwise, we will fail to reject the null hypothesis.
Technically, we never accept the null hypothesis, we say that either we fail to reject or we reject the null hypothesis. The significance level is defined as the probability of the case when we reject the null hypothesis but in actual it is true. The above figure shows that the two shaded regions are equidistant from the null hypothesis, each having a probability of 0.
The shaded region in case of a two-tailed test is called critical region. Or means that the outcome has to satisfy one condition, or the other condition, or both at the same time. Begin typing your search term above and press enter to search. Press ESC to cancel.
Skip to content Home What is the relationship between probability and inferential statistics? Ben Davis May 29, What is the relationship between probability and inferential statistics? Is probability descriptive or inferential? Is probability an inferential statistic? What is the role of probability in statistics? What are two uses of probability? How is probability used in everyday life? A sample smaller than the whole population means that we cannot guarantee that it is similar to the population.
There is a probability that it is not. We want to keep this probability of sampling error as small as possible, so researchers often set a limit of probability p of a sampling error at no more than 0.
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