1. (a)
Suppose the confidence level is .95 or 95%. When we say that we are 95% confident that the
population mean mu is within our confidence interval, what we really mean is that in long run (ie
if we made many, many confidence intervals), 95% of all possible confidence intervals will
contain the unknown population mean mu. Whether the confidence interval that we calculate
contains mu, we will never know. But, we do know that 95% of the time, the formula xbar +/- t x
s/sqrt(n) will give us a good confidence interval (on that contains mu) 95% of the time.
(b)
Note: The question says "assumption". But, to construct a t-CI for mu, we must the following 3
assumptions:
To use the t-distribution, we must assume that (1) our sample is randomly sampled, (2) the
population standard deviation is unknown and (3) the response variable is normally distributed.
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I hope this helped. If you have any questions, please ask them in the comment section. :)
Solution
(a)
Suppose the confidence level is .95 or 95%. When we say that we are 95% confident that the
population mean mu is within our confidence interval, what we really mean is that in long run (ie
if we made many, many confidence intervals), 95% of all possible confidence intervals will
contain the unknown population mean mu. Whether the confidence interval that we calculate
contains mu, we will never know. But, we do know that 95% of the time, the formula xbar +/- t x
s/sqrt(n) will give us a good confidence interval (on that contains mu) 95% of the time.
(b)

2. Note: The question says "assumption". But, to construct a t-CI for mu, we must the following 3
assumptions:
To use the t-distribution, we must assume that (1) our sample is randomly sampled, (2) the
population standard deviation is unknown and (3) the response variable is normally distributed.
----------------
I hope this helped. If you have any questions, please ask them in the comment section. :)