The exercise here: https://github.com/OpenIntroStat/openintro-statistics/blob/master/ch_summarizing_data/TeX/review_exercises.tex#L5
has a solution here:
|
(c)~The new score is more than 1 standard deviation away from the previous mean, so |
But the justification is incorrect.
The update equation for the unbiased sample variance, supposing n-1 old measurements, and given the mean and sample variance on n-1 measurements, and a new nth measurement is:
(you can see this is identical to the second equation at https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Welford's_online_algorithm)
So the critical value of x_n so that the sample variance stays the same is
therefore, the there is a factor of 25/24 missing in the justification. I would submit a pull request, but I am not sure if the textbook covers these equations.
The exercise here: https://github.com/OpenIntroStat/openintro-statistics/blob/master/ch_summarizing_data/TeX/review_exercises.tex#L5
has a solution here:
openintro-statistics/extraTeX/eoceSolutions/eoceSolutions.tex
Line 381 in 70b58fc
But the justification is incorrect.
The update equation for the unbiased sample variance, supposing
n-1old measurements, and given the mean and sample variance onn-1measurements, and a newnth measurement is:(you can see this is identical to the second equation at https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Welford's_online_algorithm)
So the critical value of
x_nso that the sample variance stays the same istherefore, the there is a factor of
25/24missing in the justification. I would submit a pull request, but I am not sure if the textbook covers these equations.