Answer:
95% confidence interval on the true mean error rate = [4.57 , 4.63] .
Step-by-step explanation:
We are given that to examine a particular program, a simulation of 1000 typical loans is run through the program. The simulation yielded a Mean,
= 4.6 errors with a Standard deviation,s = 0.5.
Since, here we know nothing about population standard deviation so we will use t statistics quantity here i.e.;
~
where,
= sample mean
s = sample standard deviation
n = sample size(no. of simulations)
= population mean or true mean
So, 95% confidence interval on the true mean error rate is given by;
P(-1.96 <
< 1.96) = 0.95 {because at 5% significance level t table gives
value close to 1.96}
P(-1.96 <
< 1.96) = 0.95
P(-1.96 *
<
< 1.96 *
) = 0.95
P(-Xbar - 1.96 *
<
< Xbar - 1.96 *
) = 0.95
P( Xbar - 1.96 *
<
< Xbar + 1.96 *
) = 0.95
95% Confidence interval for
= [Xbar - 1.96 *
, Xbar + 1.96 *
]
=
= [4.57 , 4.63]
Therefore, 95% confidence interval on the true mean error rate is [4.57 , 4.63] .