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The population mean value cannot be used in computing a confidence interval for itself. It is unknown, and, if known, what would be the point? You don't need a confidence interval for a known value.
Yes, the standard error (se) is the (estimated) standard deviation of the sampling distribution of the sample mean. That is used in construction of the CI, but does not imply what you think.
From the comments:
Confidence intervals for the mean are for the population mean. For a normal distribution the sample mean is in the center of the interval. So it is always in the interval regardless of the confidence level. The confidence level refers to the percentage of the cases in the long run that such intervals will contain the true population mean. – Michael Chernick
When we are making inference about the population we use the sample point estimate and it’s confidence interval If we are comparing sample mean to a known population mean, we calculate the confidence interval for the population and then we check whether the sample mean that we calculated lies within the population mean confidence interval of a certain confidence level. Dr. Rana Jaber
As the title says, I'm so confused by the concept. I've read so many explanations for the concept for the past few hours and I'm even confused than when I started, because a lot of the explanations seem to be contradictory.
R-bloggers states:
It is not the probability that the true value is in the confidence interval.
We are not 95% sure that the true value lies within the interval. (to me this means that we can't say with 95% confidence that the true value lies within the interval)
Here'sn example of several comments I've read that support these statements:
u/TokenStraightFriend
" Building off that because I only recently came to grips with what exactly "95% confident" means. It does NOT mean that there is a 95% chance that the true population average is within that range. Instead, if we were to repeat our sample taking, measuring, and averaging, we expect for 95% of the time the average height we find will be within that range we predescribed. "
Yet other comments contradict this
"So let's say you want to be 95% confident, so mostly certain, but with just a small degree of uncertainty. Then z=1.95, so we can say that the average population height is somewhere between 69-3(1.95) and 69+3(1.95) inches tall"
Is that not directly contradictory to what R-blogger states?
Here's an explanation from Eberly College of Science:
"
Rather than using just a point estimate, we could find an interval (or range) of values that we can be really confident contains the actual unknown population parameter. For example, we could find lower (L) and upper (U) values between which we can be really confident the population mean falls:
L < μ < U
And, we could find lower (L) and upper (U) values between which we can be really confident the population proportion falls:
L < p < U
"
Notice they say population and not sample. The distinction is made super clear in the Eberly college example.
I keep reading this idea that if you were to construct an infinite number of confidence intervals at a single confidence level 95%, 95% of those intervals may contain the true value for the parameter. That sort of explains what a confidence level is to me, but I don't understand when someone tells me 'this specific confidence interval has a confidence level of 95%'.
My doubt is how can i interpret the concept of confidence and confidence interval. When we are saying 95% confidente we say that in theory, we expect that for a 100 different samples, 95 are going to have the value of the paremeter inside our confidence interval, but then if someone says that something lasts for more than 100 hours and i have a 95% confidence interval in the form of (90, 110), we say that it is false what the person say
So can someone give me a more specific way of how to interpret a confidence interval after i found it
Edit: It was a one sided test, not two sided