Question

Explain confidence intervals and hypothesis tests in terms that a 4th grader could understand. Include 2–3 tips and tricks for how you would determine which type of inference you are working with (confidence interval estimation or hypothesis testing).

In addition, explain the concept of the p-value in hypothesis testing. Since the p-value is commonly output from data analysis software when conducting a hypothesis test and is reported in study results and articles, it is important to understand not only how to use a p-value to make a decision for a hypothesis test but also what it is and how to interpret it. Answer the following questions about p-values in hypothesis tests:

What does the p-value tell you?

How can it be used or interpreted?

What questions or issues do you have related to the concept or use of p-values in hypothesis testing?

Answer 1

Soln,

To understand Hypothesis and cnfidence interval in naive way we must understand what is statistics,

First of all we need to understand that in probability and statitistics Nothing is certain and accurate hence we will only assume the happening as per previous data given or analysis done. In statistics we create a situation which shows a pattern of things had occured and hoped that most probabily the same way it will occur again but it is naot certain rule that the thing will happen for sure there is a amount of uncertanity always.

For this A concept of Confidence interval was made , lets say a a statements says that at 95 % confidence level create a population mean confidence interval.

It simply mean that when we conduct a experiment several times then we make a interval of mean which shows that 95 % of the experiments conducted says that the population mean will occur between certain given set of Confidence intervals.

lets say when we conduct a experiment it shows the mean value of experiment as 4, 4.1, 4, 4.3, 4.03, 4.02, 4.3, 4.06, 3.99, 3.98 then it is clear that the population mean will range between 3.8 to 4.3 and this range happent 95 % of the experiment conducted.

Now comes hypothesis testing for this we need to understand a simple example,lets say a choclate company produces a choclate of 5 gm each as per the supervisor of thr factory, but wheen you weigh 10 or 20 or 50 choclates you find that the weight of choclate each time was little or sometimes way different from what supervisor claims, then to check wether the supervisor is correct or not we conduct a hypothesis test in which we use a null hypothesis. we never prove ourselves as correct we always check wether we are able to reject the hypothesis we made or do we fail to reject our hypothesis, hence in the above stated example we take our null hypothesis as Supervisors claim of 5 gm and then we check wether we have sufficient evidence to reject supervisors claim or do we fail to reject supervisors claim.

For this testing we uses p value which shows the probability of happening that hypoyhesis. If the probabilty of happening is very low say 0.0001 then we will reject our hypothesis and if the probability or chance of happening that claim is sufficient enough that we cannot ignore that claim then we fail to reject, for this we compare the probabilty value of our hypothesis with the level of significance value which id the critical area in which we reject the hypothesis, so if the p value of our hypotheis is small in compared to the alpha value then we can evidently reject and if it is grater than alpfha value theen we fail to reject.

The p value tells the chance of happening our hypothesis. It can be found by First finding the Z score which shows that how far the data set is away from the mean of the data set in form of no of standard deviations.after finding the Z scores or t scores we can look into Z or t table which always shows the area of the bell curve left to the Z point vaue further this Area is considered as p values and which is further compared with level of significnce values to reject or fail to reject.

One main thing we must consider in our mind while making a conclusion that we never accept our hypothesis directly we can only reject ot we fail to reject.