My question is almost exactly the same as another one here on math stack exchange, but it isn't as explanatory as I'd like it to be with some parts. I was unsure of whether or not it'd be "okay" to repost the question, especially since the other one was asked about three years ago.
An electric scale gives a reading equal to the true weight plus a random error that is normally distributed with mean 0 mg and standard deviation = 0.1 mg. Suppose that the results of five successive weighings (in mg) of the same object are as follows: 3.142, 3.163, 3.155, 3.150, 3.141.
a) Compute a 95 percent confidence interval estimate of the true weight. b) Compute a 99 percent confidence interval estimate of the true weight.
Based on the answer that was given, we first find the sample mean, which is just: $(3.142+3.163+3.155+3.150+3.141)/5.$
Then, we find the standard deviation, which is where I get some confusion. We're supposed to use the "other" standard deviation, but I don't know what the differences would be. The apparent "new" standard deviation would be:
std deviation = $(1/\sqrt5) * .1$
Then, we multiply that by plus or minus 1.96. However, I am completely confused as to how 1.96 is obtained. There is a table we can consult, but it seems that there are different tables depending on whether or not the confidence interval is two-sided - in which case, how would we know if the CI is two-sided?
I hope I'm being clear enough here, a slow explanation would be very helpful.