2. subtract the sample median from its respective sample data
> diffmeterusage = meterusage - median(meterusage)
> diffnometerusage = nometerusage - median(nometerusage)
Feel free to look at your vectors that contain (
X
i,Meterusage
−
tildewide
X
Meterusage
) and (
X
j,Nometerusage
−
tildewide
X
Nometerusage
)
3. Take the absolute value of these differences:
> abdiffmeterusage = abs(diffmeterusage)
> abdiffnometerusage = abs(diffnometerusage)
Now type
abdiffmeterusage
and
abdiffnometerusage
and compare the data appearing in these
data vectores to
diffmeterusage
and
diffnometerusage
.

c
circlecopyrt
Jim Stallard 2018
3
4. Conduct a two-sided “Pooled”
T
-test on the data appearing in the ‘absolute differences from the
sample median” data vectors you created in the previous step:
> t.test(abdiffmeterusage, abdiffnometerusage, alternative="two.sided", var.equal=T)
What do you notice? You should get a test statistic in the neighbourhood of
T
Calc
=
−
2
.
34 (-2.3413) and a
P
-value of
0.02487
. Does the result of Levene’s test support your commentary in Lab Exercise 1(d)?

Lab Exercise 2:
Referring to Lab Exercise 1: Consider the sample taken from households that have water
meters. Does the sample of 22 households indicate that the standard deviation in the monthly water usage
is less than 5 meters
3
? Test using
α
= 0
.
01.
Lab Exercise 3:
Recall Lab Exercise #4 from last week’s lab, Lab Seven.
You were asked to test the
following hypotheses:
H
0
:
p
≥
0
.
98
H
A
:
p <
0
.
98
based on a random sample of
n
= 125 items and a presumed value of
α
= 0
.
05.
It was found that
hatwide
p
=
118
125
= 0
.
944,
Z
Calc
=
−
2
.
875 and the
P
-value can be verified to be
0.00202
.
(a) Assuming that statistical testing is to be done at
α
= 0
.
05, for what values of the sample proportion
would H
0
be rejected in favour of H
A
?
That is, find the
critical value of
the sample proportion,
hatwide
p
critical
.
(b) Suppose 94% of all items produced by this manufacturing process are of satisfactory quality. Using
your result in (a), find the probability that you will conclude from
n
= 125 that the proportion of
items produced by this manufacturing process that are of satisfactory quality is
at least
98%.
(c) If the quality control inspector were to select a sample size based on
α
= 0
.
05 and
β
= 0
.
10, how many
items would he randomly select?
Lab Exercise 4: