Question 1 If 100 random samples of size n were drawn and, if, for each, a 99% confidence interval for m was computed, then exactly 99 of these confidence intervals would contain the true population...

Question 1
If 100 random samples of size n were drawn and, if, for each, a 99% confidence interval
for  was computed, then exactly 99 of these confidence intervals would contain the
true population mean within their limits. Elaborate.
Answer:
The statement mentioned above that “if 100 random samples of size n were
drawn and, if, for each, a 99% confidence interval for  was computed, then
exactly 99 of these confidence intervals would contain the true population
mean within their limits” is a true statement. The 99% percentage
confidence interval does not mean that the population parameter ‘’ lies in
that interval with 99% probability, rather it is mean 99 of 100 such interval
would include population mean within their limit. The confidence interval is
used to measure the reliability of an estimate and varies, in principle, from
sample to sample as it is an observed interval and therefore a 99%
confidence interval does not mean that there is 99% probability that the
population mean would lie within that limit. Moreover, confidence interval is
used to determine the frequency with which an observed interval would
contain the parameter and therefore 99% confidence coefficient measures
the proportion of total intervals which would contain population mean within
its limits.
Question 2...