1. What is meant by “Confidence Level/Coefficient” and why is it different than

Question

1. What is meant by “Confidence Level/Coefficient” and why is it different than “Confidence Interval”?

ANSWER: Good job, everyone! Let me summarize and expand a little with an example.

Confidence interval is the “interval estimate” that with the probability equal to confidence level contains the true population parameter (e.g., population mean) using +/- certain value (i.e., margin of error) of the sample statistics (e.g., sample mean).

I will use an example to explain these concepts. Let’s assume we are interested to find out what is the average weight of a population of 1000 marbles of different sizes and materials, i.e., we are interested in estimating population mean. However, we don’t have enough time and budget to measure the weight of every marble, add them up, and divide the sum by 1000 to directly calculate the population mean. So …. we take a sample of size 40, and calculate the sample mean. Our sample mean is a point estimate of our population mean. Let’s assume our sample mean turns out to be 10.5 oz. We also know that due to sampling error, our sample mean will be close to the population mean but will not be equal to it. Further assume, our margin of error E for a 95% confidence level is 1 oz.

Confidence Level = 95%

E = 1 oz for a confidence level of 95%
Confidence Interval = Sample mean +/- E
Confidence Interval = 10.5 +/- 1 = [9.5 to 11.5]
Since our confidence level was 95%, we are 95% confident that the interval [9.5 to 11.5] contains the true average weight of 1000 marbles, i.e., our population mean. Or differently stated, there is 0.95 probability that the average weight of 1000 marbles is equal or greater than 9.5 oz but less than or equal to 11.5 oz.

In general, confidence interval is the “interval estimate” that with the probability equal to confidence level contains the true population parameter (e.g., population mean) where the interval is +/- certain value from the sample statistic (e.g., sample mean). In the above example:

Interval estimate = [9.5 oz to 11.5oz]
Confidence level = 95%
Population parameter = population mean aka, target parameter
Sample statistic = sample mean
Sample statistics +/- Certain value ==> Sample mean +/- E

Any questions? Look for a follow-up question, "Q2: Confidence Level and Confidence Interval."

2. How wide our confidence interval should be if we want our level of confidence to be 100%? Why?

Please see the previous questions and responses on "Confidence Level & Confidence Interval" before you attempt to answer this question.

Please Type answer.

Explanation / Answer

To be 100 percent confident, our confidence intervel should be 100 percent wide. It means all the possible values are to be considered. In the example given above, all weights of 1000 marbles is to be considered. Only then we will get all possible values in the interval. However, when we consider all the weights instead of taking sample, we can directly get the population mean, that is, average weight of 1000 marbles and so no question of confidence interval or simply interval. Observe the difference between interval and confidence interval. Interval means some range of values wherein our desired value, say X lies or belongs to such interval. Here, we did not mention any confidence level. But when we say that we are 99percent confident that our desired X value lies in a certain interval, then such interval is called as Confidence Interval and in this case it is 99percent confidence interval. We do not mention the word confidence when we are 100percent sure. It means 100 percent confidence level interval is simply called Interval rather than saying Confidence Interval. So, there is nothing called 100percent confidence level when we have to know the width of interval as at 100percent, we get the single accurate value as the answer rather the value lieing in an interval.

If you take 999 marbles as sample and find sample mean, you cannot say you are 100percent confident that it matches with the population meanmean becausecause there is alsoalso possibility that it does notnot equal the population mean, even it is notnot close to population mean if the otherother marble you did not taketake into sample is of extreme weight, eithereither extreme low or extreme high. So, you can be atmost 99.99 percent confident but not 100percent. So, one should never use 100percent confident level as one cannot be such confident because there is the chance of going wrong if one is 100percentpercent confident.

Hence, the most used confidence levels are 90, 95 & 99 Percent. The more the confidence level, the wider the confidence interval. For example, At 95percent CL, interval is 10 to 20 & At 99percentpercent CL, interval is 5 to 25. TheThe wideness should be on both sides, stretched to left and right.

  Hope it helps. Good luck.

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.