Fu-Bun
Bank conducts a sampling investigation to to learn its customers degree
of satisfaction every year. The sample size is 100, and the result of mean
is about 80 percents. According to the historical information (from 1990
to 1999), Fu-bun bank knew the variance is about 400. Now we want to know
the all customers how they satisfied Fu-Bun¡¦s service. We could use the
skill, ¡§estimation¡¨.
We
should know some tips about solving statistical problems like that by excel.
There
are three kinds of estimations as following; however, basically, I just
could solve this problem because I just have this information of Fu-Bun
bank case from Taiwan. But anyway, I will introduce the other two estimations
for you.
First,
let me show the study of the Fu-Bun one.
1.
Choose the function button, ¡§fx¡¨.
2.
Select ¡§Statistical¡¨ and ¡§Confidence¡¨. And click ¡§OK¡¨.
3.
As usual, we use 95% confidence interval for sure our inference is right.
That
means our alpha is 0.05, and the standard deviation is the square root
of 400.
That¡¦s
equal to 20. The size is 100.
4.
And then we got the answer is about 3.92. By the formula of Z, we knew
the confidence interval would be between 80-3.92=76.08 and 80+3.92=83.92.
5.
Now I want to introduce another estimation¡XStudent¡¦s T-distribution.
First,
we should select ¡§statistical¡¨ and ¡§TDIST¡¨ under the ¡§Function¡¨ screen.
Then click ¡§OK¡¨.
6.
Then we can see the screen. I just try the probability of t-distribution
under the 5 degree of freedom (this is the only parameter in t-distribution).
The tails we could choose are 1 or 2. depend on what situation we meet.
7.
This answer is about 0.05. That means the probability over 95% confidence
interval of t-distribution (alpha-value.) has a t-value is 2.015.
8.
Of course, I have said that before. This is the same as Z-distribution
(standard normal distribution). So we can find out the inverse value of
t-distribution. By the way, the shape of t-distribution is symmetry like
the normal distribution.
9.
But we should watch out the difference using between ¡§TDIST¡¨ and ¡§TINV¡¨.
We could
choose 1 or 2 tails under ¡§TDIST¡¨ screen but ¡§TINV¡¨. The probability
under the ¡§TINV¡¨ function is two tails.
10.
We got the answer we want. This is the inverse value of 0.05(alpha value.)
under t-distribution.
11.
The last important distribution is chi-square, select ¡§CHINV¡¨ and ¡§Statistical¡¨
under the ¡§function¡¨ screen. The use of ¡§CHIDIST¡¨ is the same as the
other two, so I want to skip it.
12.
By the way, I should tell every one that the shape of chi-square is not
symmetry. So if we find out one inverse value in the certain probability
and certain degree of freedom, it will not be the same as the other side
of the shape of the chi-square distribution. We could realize that by the
following pictures.
