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As confidence interval says "95% confidence interval indicates that 19 out of 20 samples (95%) from the same population will produce confidence intervalS that contain population parameter.It means the confidence interval treat their bounds as random and the parameter is fixed.

Then how do we get lower and upper bound of our statistics if it is random not fixed?

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  • $\begingroup$ The random part becomes the observed data. $\endgroup$ – Michael Chernick May 26 '18 at 16:35
  • $\begingroup$ @MichaelChernick can you elaborate it more please? $\endgroup$ – user172500 May 26 '18 at 16:43
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    $\begingroup$ Before collecting the data the confidence interval is defined in terms of random variables. After you collect the data those random variables are observed values. So the endpoints of the interval are determined. As an example a confidence interval for the mean of a normal distribution depends on the sample mean and sample variance which are random variables. Given the observed data these random variables become fixed values. $\endgroup$ – Michael Chernick May 26 '18 at 17:05
  • $\begingroup$ please correct me after observing a sample mean height of women in "X" city is 5 feet between 4.8 and 5.2 feet. From now on based of this sample determination of lower and upper bound 19 out of 20 samples will contain 5 feet height of women Or 19 out of 20 will lie between 4.8 and 5.2 feet? $\endgroup$ – user172500 May 26 '18 at 17:31
  • $\begingroup$ In referring to a 95% confidence interval the definition is that if you repeat the process of generating such confidence interval 20 times you would expect that about 19 will contain the population mean and 1 will not. The exact number does not have to be 19. Rather you are guaranteed that as the number of times you repeat this process gets very large the percentage containing the population mean will be very close to 95%. $\endgroup$ – Michael Chernick May 26 '18 at 18:42

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