How Does t0.975 Give a 95% Confidence Interval?

In summary: If you have a table that tells you the percent of the data between a given number and the mean, and you want a 1-sided interval, from a sample of size N, then do this:First go to the row N-1 , since you have N-1 degrees of freedom when your sample is N. Then look up the column value c/2 on the table, e.g, if c=0.95 ( for a 95% confidence interval). That is your t_c value.
  • #1
moonman239
282
0
Hi!

I'm reading up on confidence intervals for means. This is leaving my mind boggled. I caught the part where the interval = tc*(sample standard deviation/the square root of n). What's boggling my mind though is the variable tc. I see that t refers to a T distribution. But, I can't figure out how t0.975 could give you a 95% confidence interval.
 
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  • #2
The 95% confidence interval for a mean is between t_0.025 and t_0.975.
 
  • #3
Okay thanks. The page I'm reading makes reference to another page, which then refers to an appendix, neither of which helped.
 
  • #4
So how do I get the value of Tc for a certain confidence interval?
 
  • #5
"So how do I get the value of Tc for a certain confidence interval? "

Look at the t-table (not stuttering; it is a table of t-values:smile:). It then depends if
your interval is 1-sided or 2-sided. Unfortunately, there are different table formats
too. If your table deals with standard errors (which you use in case you don't know
the pop. standard deviation) .

If you have a table that tells you the percent of the data between a given number
and the mean, and you want a 2-sided interval, from a sample of size N, then do this:

First go to the row N-1 , since you have N-1 degrees of freedom when your sample
size is N. Then look up the column value c/2 on the table, e.g, if c=0.95 ( for a 95% confidence interval). That is your t_c value.

If you give me more details, and a link to the type of table you are using, we
can work out a specific example.

HTH
 
  • #6
My table has the Tc values from top to bottom and degrees of freedom from left to right. Must be one-sided because your directions don't agree with my table.
 
  • #7
My table is not on the Internet - I'm reading a book called Probability and Statistics from Schaum's Outlines. (this is not homework)
 
  • #8
O.K , let me go back home and check it out, I don't have it here with me.
 
  • #9
FYI, one can google the following: student t distribution table

Here is the first hit:
http://www.math.unb.ca/~knight/utility/t-table.htm​
I like that it shows both the one-tailed and two-tailed values.
 
Last edited by a moderator:
  • #10
OK, how do I use it?
 
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FAQ: How Does t0.975 Give a 95% Confidence Interval?

What is a confidence interval for a mean?

A confidence interval for a mean is an estimate of the range within which the true population mean is likely to fall. It is calculated using sample data and is typically expressed as a range of values with a specified level of confidence, such as 95% or 99%. This means that if the same population was sampled multiple times, the calculated confidence intervals would contain the true population mean in 95% or 99% of the samples.

How is a confidence interval for a mean calculated?

A confidence interval for a mean is calculated using the sample mean, standard deviation, sample size, and a specified level of confidence. The formula for calculating a confidence interval for a mean is: sample mean ± (t-multiplier * standard error), where the t-multiplier is determined by the sample size and desired level of confidence. The standard error is a measure of the variability of the sample mean and is calculated by dividing the sample standard deviation by the square root of the sample size.

What level of confidence should be used for a confidence interval for a mean?

The level of confidence used for a confidence interval for a mean is typically chosen by the researcher based on the desired level of precision and risk. A 95% confidence interval is commonly used, meaning that there is a 95% probability that the true population mean falls within the calculated interval. However, a more conservative level of confidence, such as 99%, may be used if the consequences of being wrong are significant.

How does sample size affect the width of a confidence interval for a mean?

As sample size increases, the width of a confidence interval for a mean decreases. This is because larger sample sizes result in a more precise estimate of the true population mean. As a result, the standard error decreases, making the confidence interval narrower. In other words, larger sample sizes provide more information and reduce the margin of error in estimating the true population mean.

What are the limitations of confidence intervals for means?

Confidence intervals for means have several limitations, including the assumption of a normal distribution and the need for a large enough sample size. If the sample is not normally distributed or if the sample size is too small, the calculated confidence interval may not accurately represent the true population mean. Additionally, confidence intervals do not provide information about individual data points, only the range within which the population mean is likely to fall.

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