Define Confidence interval in a very layman manner with example
Question
Confidence interval is something for which you can get N number of definitions, but what really matters is whether you understand the concept or not.
Try to take any simple real life example and explain the concept.
These are the basic questions asked in interviews and the interviewer is not looking for a standard definition. The moment you ‘recite’ the definition, he/she will ask for an example.
The easier the example, the better the impact
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Let us assume that we are analyzing the marks of students in a university consisting of 1000 students. This list of 1000 students is called the population. It requires large effort and time to analyze the data of entire students. So we simply take a sample of 10 students from this population and assume that the inference we get through analyzing the sample is also applicable to the population. But before accepting these criteria, we need a statistical test to prove or believe that the result from the sample is matching with the population without much error. This can be determined with the help of several statistical tests . Once we find the mean, median for avg marks for all the 10 students, we can assume the same for 1000 students. But will that be true for 1000 students? We have 2 possibilities that we convert them into hypothesis, null and alternate hypothesis. Stating null- we can say avg marks can be less than 5 for the total population and for alternate we can say it can be more than 5 marks for the total population.If i say- I am 85% confident that my null hypothesis will not be rejected.So this makes a magnitude for belief/trust/chance that we have in terms of percentage. So confidence level is used for demonstrating this chance in terms of percentage.
While estimating a population parameter , its always preferred to provide it as a confidence interval(CI).
CI tells us the range in which our population estimate lies. For example, if we need to determine the average weight of students in a school, we will take a sample and calculate its mean weight (let it be 35kg).
Next, we will construct a range : 31 to 39kg. This is CI which tells us that the true mean weight of the population will lie in this range. The lower and upper limited is decided by the sample size, sample variation and the CI (say 95%). So we are 95% confident that the average weight of the entire school students will lie between 31 to 39kg.
If the sample is small, then the mean will vary hugely with other samples(sampling error) and the CI will increase. And if the weight of the students we picked as a sample varies a lot, then also the CI will increase.
Confidence interval is basically the range of values within which the population parameter lie with certain probability.
For example: A bikaji sells its bujia in the pack of 500g. But if you take suppose 10-15 different packets of bujia, some of the packet will weigh 500g , some will weigh 499g, some will weigh 503g etc. In 10-15 packets there is very less chance that bujia will be exactly 500g. Anyone can put a lawsuit on bikaji for not delivering 500g as promised but if you see the description they have put the margin of error in the description which tells that within this interval the weight of the bikaji bujia lies. Because of this no one can put the lawsuit against bikaji.
Confidence interval is basically the range of values within which the population parameter lie with certain probability.
For example: A bikaji sells its bujia in the pack of 500g. But if you take suppose 10-15 different packets of bujia, some of the packet will weigh 500g , some will weigh 499g, some will weigh 503g etc. In 10-15 packets there is very less chance that bujia will be exactly 500g. Anyone can put a lawsuit on bikaji for not delivering 500g as promised but if you see the description they have put the margin of error in the description which accounts for the variation and which tells that within this interval the weight of the bikaji bujia lies. Because of this no one can put the lawsuit against bikaji.
Confidence Interval is the range of values where population parameter lie. you’ll probably be finding confidence intervals using the normal distribution. But in reality, most confidence intervals are found using the t-distribution (especially if you are working with small samples). The confidence intervals generally are 0.95 which tells 95% of the time your predicted paramater is close to the population parameter
Suppose we have a product and we are claiming something about our product like its weight or its accuracy or anything but In real life, we can’t sure 100% for anything so we make an interval a range by which we can say that our claim will fall in this range and we called it confidence interval.
Suppose we have a product and we are claiming something about our product like its weight or its accuracy or anything but In real life, we can’t sure 100% for anything so we make an interval a range by which we can say that our claim will fall in this range and we called it confidence interval.
Confidence interval is the range of values where we say that the mean value of the sample lies in that range with a certain probability.
Ex: my bag weighs in range of 99-101 kgs with 95% confidence interval, if I claim that my bag weight is 100 kg it’s correct
Confidence Interval in simple terms tell how much uncertainty lies within a statistics. It gives us how much is the probability that results from particular statistics will lie particularly within that interval.
Ex: 50% confidence level means the number of time we repeat a experiment on same statistics , probability will be 50 times out of 100 times that it will lie within confidence level
It is simply the interval of values between which I am confident that my population statistic would lie.
For example, 95% confidence interval means that I am 95% confident that my population value would lie within the said interval.
In real-life scenarios, many times getting a range of values makes more sense than a single value representative of the whole population.
For instance, if we want to figure out the proportion of female babies born in a year on average, giving a single value (point estimate) doesn’t give us much information and might be considered as a heavily biased number. In such cases, we need something that can provide us with a range of values with a certain percentage of assurance. So, obtaining a range of values with a specific percentage of confidence is the confidence interval. ‘The word ‘confidence’ implies the level of certainty or level of assurance that can be given for the found range of values.
Now, if I say that the proportion of female babies born in a year lies in the interval (0.46,0.52) with 95% percentage assurance, this provides us more information. This range is calculated around the average values itself that we talked about in the above case.
If we want a more certain range of interval, the number of values contained in the interval, or in other words, the width of the confidence interval will increase in order to accommodate any more values that could be possible for the proportion of female babies in a specific year.
A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.
Suppose a student measuring the boiling temperature of a certain liquid observes the readings (in degrees Celsius) 102.5, 101.7, 103.1, 100.9, 100.5, and 102.2 on 6 different samples of the liquid. He calculates the sample mean to be 101.82. If he knows that the standard deviation for this procedure is 1.2 degrees, what is the confidence interval for the population mean at a 95% confidence level?
It is possible to calculate the average height of a school or a class. Simply take the data and calculate the average.
But how will you calculate the average height of Indian males. It is impossible to get the heights of all Indian males. So we take a sample. Since we have taken the sample the average height of the sample will not be exactly equal to average height of Indian males. It will be either little less or little more, depending upon your quality of sampling.
So instead of giving the exact value, we give a range and attach a confidence interval with it. For e.g 95% C.I means we are 95% confident that actual average height of males will lie in that range.
Definition: A x% confidence interval is an interval, which is able to catch the true parameter with x% of probability.
For example you want to calculate the average salary of all the employees of your company, but you can ask salary from just people of your branch only. So using this data you will create a confidence interval which will contain the true value (that is average salary of whole company). Bigger the percentage of confidence interval wider will be its length.
Confidence interval shows us the likely range of values of our population
sample Interval 😡
margin of error: E
E=z(aplha/2)*S.D/square root(n)
-alpha=1-confidence level
confidence level=1-alpha
suppose confidence level =95==> alpha=1-0.95 ==0.05
There are two terms:
1) level of significance= size of critical region
2) Confidence interval: 1-Level of significance
Example: Let suppose a student is expecting 95% marks in exams to get a video game from his parents. If he will score less than that he wont get video game.
here critical region is= 100-95%=5%
confidence interval is = 95%
If he score 94% then we can clearly say that our null hypothesis got rejected here due to smallest level of significance because critical region > expected critical region (6%>5%).