Practical example – confidence interval
Hi,
I have a couple of questions related to the practice example at 6:30 where they used the frequency distribution tables of the shoes for USA based on different sizes.
1- for shoes size 6 the confidence interval was calculated and it's between [1.8-4.04].
I thought the confidence intervals only apply for normal distribution? and for shoes size 6 (line number 8) I don’t see that the distribution is is normal? how is that? can someone please clarify to me?
I know that, if the sample distribution is not normal, we can use the CLT, which means the average of sample. How can we apply that for shoes size 6 (line 8)
2- why the standard error was calculated? I thought the standard error only apply for the sample of means (CLT) and in line 8 the data are not mean but normal distribution.
thanks,
haithem,
Confidence intervals do not require the data itself to be normally distributed. Please revisit the lesson about The Central Limit Theorem.
It basically ensures that the sampling distribution of the mean is approximately normal if the sample size is sufficiently large. For shoe size 6, the confidence interval is valid if the sample size is large enough, even if the raw data is not normally distributed.
Best,
Ned