(Specify the form of the null distribution, the mean and the standard
deviation, you do not need to solve for numerical value of the standard deviation).
< 0.5

4.7
Is this a
one-tail
or
two-tail test?
(circle one)
4.8
We would reject the null when our test stat is
greater than/
less than/
equal to
_-1.64______.

Practice Final
6
You want to calculate the power of this test against your alternative hypothesis, that the true proportion is
25%.
To do this, you will need to calculate
?
????
--
the critical value of p under the null hypothesis for α=0.05.
Set up the formula you would use to solve for
?
????
.
4.9
Formula for
?
????
?
????
= ?
0
+ ?
????
√
?
0
(1 − ?
0
)
?
; ?
????
= ?
0.05
4.10
With plug in values
?
????
= 0.5 + (−1.64)
√
0.5 (1 − 0.5)
200
= 0.44
Draw the distributions of the null and the specific alternative hypothesis, and label each.
Label the
following values of on the x axis:
?
0
, ?
𝐴
, ?
????
(IMPORTANT
–
EACH OF THESE LABELS WILL BE WORTH 1
POINT).
Shade in the appropriate area that represents the power of the test. The drawing does not have
to be the right scale, but the ordering of the values on the axis needs to be correct.
(This part of the
problem is not in Aplia)

Practice Final
7
Set up the formula for calculating power, and plug in the values.
4.11
Formula for the power of this test:
????? = ??
(
𝑍 <
?
????
− ?
𝐴
√
?
𝐴
(1 − ?
𝐴
)
?
)
4.12
With plug in values:
??
(
𝑍 <
0.44 − 0.25
√
0.25 (1 − 0.25)
200
)
= Pr(𝑍 < 6.3) ≈ 1
Challenge:
If you choose the critical value of the test as your specific alternative hypothesis, what will your power always be?

Practice Final
8
Problem 5. Statistical inference for means
Newly developed diet pills are known to work differently for men and for women. A sample of 120 subjects (50 males,
70 females) participated in this study, in which their pre- and post-treatment weights were measured:
Male (N=50)
Female (N=70)
Pre
Post
Difference
Pre
Post
Difference
mean
207
202
-5
165
155
st dev
8
6
10
9
Our first goal is to test the claim that there is an effect of the diet pills for females.
Let
?
̅
𝑓
be the sample mean difference
for females, and
?(?
̅
𝑓
)
be the population parameter:
-10
12
15
𝐻
0
:
?(?
̅
?
)
= 0
vs
𝐻
𝑎
:
?(?
̅
?
)
< 0