some trouble with the following question...
I'm starting to study stats and R again after almost a year, so I
thought this is interesting. I think I have the answer. Here is how I
arrived at it:
Generate 100 standard normal N(0,1) samples of size 100,
X1(k),...,X100(k) > where k=1,...,100 (The k is and indicie in brackets)
Calculate the sample mean for each sample. > > For each sample mean
Xbark the 0.95-confidence interval for the mean mew=0 > is given by...
Ik= ( Xbark plus or minus 1.96/10) > > Find the number of intervals
such that 0 does not belong to Ik. How many of > them do you expect to
see? > > Well so far I have come up with... > > N<-100; Nsamp<-100 >
A<-matrix(rnorm(N*Nsamp,0,1),ncol=Nsamp) > means<-apply(A,2,mean)
This looks fine. Now you have to figure out I_k, the confidence
interval. According to your formula for this, the lowest boundary in I_k
must be XBar_k - 0.196, and the highest boundary XBar_k + 0.196. Now you
have to figure out how many times 0 falls outside this interval. In R
terms, XBar_k is your `means' variable. So you want to know how many
times means - 0.196 > 0 or means + 0.196 < 0.
A previous poster said that sum() counts the number of times something
occurs if you're dealing with boolean data i.e. 1s and 0s, or TRUEs and
FALSEs. R gives you these TRUE/FALSE values. E.g. if you have a variable
w = 2, running w > 0 will cause R to respond with TRUE. Same goes with
vector data i.e. if w = c(0,1,2,3,4), then running w > 0 will cause R to
give you, this time, a vector or TRUEs and FALSEs: FALSE TRUE TRUE TRUE
TRUE. Then, running sum(w>0) will count only the TRUEs and give you 4.
(Actually, R pretends it's a vector of 1s and 0s and sums it up: sum(0 1
1 1 1) is 4.)
However I have no idea what I am doing and no idea if that even
makes sense. > Any help would be greatly appreciated as I have no
experience of statistical > software whatsoever.
I hope this gives you some ideas as to how to turn your textbook
statistical concepts into R language commands. Thanks to R's vector
goodness, it's usually simpler than it seems--you don't need to
overthink it.