The estimated mean is still sum / size.

I think your question is how to figure out the confidence interval for this estimation.

Take a look here: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading23b.pdf

Thank you very much for quick reply.

Yes, query is more related to CI. I don't know the exact distribution the data set but it refers data may not normal ( difference between mean and median around 5-6 for sample size 20. Also Skewness >1, Kurtosis >1 for some sample study). I have also tried with P-P, Q-Q plot normality test ; shows weak normal distribution properties.

The document you shared discuss binomial distribution, my study related to time study (data on cycle time of process). For different product/product type it shows normal or non-normal distribution characteristics. I don't know the population mean, stad. dev as well as distribution of data for some instances.

Do you think, x ̅ ± t_(∝/2) (σ_(x )/√n) is the appropriate equation for this case also? (I know this equation holds for normal dis., my question is it good for non-normal distribution also? )

"_ " refers to subscript , σ_(x) - standard error of sampling distribution of sample mean

The section 4 of the document that I shared discusses a generic case.

It says you can use the same formula but making sure you have enough samples. Then it discusses how large n must be.

You can also check this thread where someone mentions Wilcoxon test.

https://stats.stackexchange.com/questions/112829/how-do-i-calculate-confidence-intervals-for-a-non-normal-distribution

Really, appreciate your sincere reply. Currently going through the reading materials. If I have further questions I shall leave a comment about that. Please, care to reply.

I’ve gone through few the materials, and have few important questions in my context.

(Discretion: Long comment)

For example, We’re dealing with operation time, population size -100 batches of a particular product, we’ll take at most 10-15 batches as samples. Each sample batch has a varied number of observations of the desired variable. Now, bootstrapping done on the n observed data of that particular variable for a sample; each dataset size is n (same size as observed dataset), and no of resampling is B (nearly 100) for bootstrapping.

Mean from each dataset is recorded and from there mean of resampling mean is calculated. This mean of resampling mean is treated as the sample (batch) mean. This way 10-15 batches of sample mean calculated.

Here the questions are:

1. Do all the sample need to have equal no of observations, n? Some batch has 23 observed data; some have more than 40. So, should we count up to 23 observation (min. value among samples)? Or, it doesn’t matter since after bootstrapping we’re taking mean of resampling mean.

2. Sampling distribution of sample mean needs to go through another bootstrapping? [to obtain the ultimate statistic (i.e. mean and std. dev.), to estimate a confidence interval for population parameter]

Please, care to leave a reply.

TIA

" Each sample batch has a varied number of observations".

In bootstrapping you need to do resampling with replacement yielding the same sizes of the original data. For example, if you original data is

{x_1,x_2,x_3,x_4,x_5}

resampled distribution can be as follows:

{x_1,x_5,x_1,x_1,_x2}

or

{x_3,x_1,x_5,x_5,x_4}

they should all have the same size (5 samples in this example here) and repetitions are allowed.

watch this video: https://www.youtube.com/watch?v=gcPIyeqymOU

and a bit more technical: https://www.youtube.com/watch?v=ZCXg64l9R_4

Many thanks for your cordial help.

Hi Mynur,

Solutions to that problem can be found in:

http://www.stat.tugraz.at/AJS/ausg082/082Singh.pdf

https://rstudio-pubs-static.s3.amazonaws.com/35076_9e2a8cf54d9948e1b932374cbd14aa82.html

https://en.wikipedia.org/wiki/Exponential_distribution

and so on.

Cheers,

Frank Veroustraete

Thanks, Frank Veroustraete.