Using StatCrunch: z-scores
Video: http://www.youtube.com/watch?v=8ms0v9qQuHk
Example 1:
Find the following z-scores:
According to the textbook, one uses Table A-2 to find the z-value with the desired area.
For example, we find
by looking where the area is 0.1 (or as close as possible):
Since the closest area to 0.1000 is 0.985 on the table, we find the z-score (for the left
tail) to be -1.29 (add the 0.09 at the end of the -1.2). Since we are interested in the
positive value, we conclude
BUT, there is a MUCH EASIER way to find these values using StatCrunch…
(1) Click Stat–Calculators–Normal
(2) The calculator will initially be set to the
standard normal distribution (μ=0, σ=1)
(1) To find
select “=>” (in the left box),
enter “0.1” (in the right box), then Compute.
The answer appears in the middle box (1.281…)
(2) To find
select “=>” (in the left box),
enter “0.1” (in the right box), then Compute.
The answer appears in the middle box (1.644…)
Much easier!
Let’s try doing a confidence interval this way…
Example 2:
Suppose the weights of 10-year-olds are normally distributed with
A sample of 9 children is found to have a sample mean ̅
(1) Find the 90% Confidence Interval
(2) Find the 99.99% Confidence Interval
When the population standard deviation is known, the formula for the Confidence
Interval (C.I.) of level
is
(̅
)
̅
Where
√
(1) For a 95% confidence level:
which gives
Using the StatCrunch Normal Calculator, we find
̅
̅
√
√
Thus, the 95% confidence level is (70.52, 109.68)
(2) For a 99.99% confidence level:
which gives
Using the StatCrunch Normal Calculator, we find
̅
̅
√
√
Thus, the 95% confidence level is (43.32, 136.68)
Notice the resulting confidence interval in (2) is so large we can’t infer anything from it
Indeed, if I were to compute the 99.999999% Confidence level, I would get (21.23, 158.77) Ridiculous!