1
EXERCISES:
KEY
1. Suppose medical researchers think that 0.70 is the proportion of all teenagers with high blood
pressure whose blood pressure would decrease if they took calcium supplements. To test this
theory, the researchers plan a clinical trial (experiment) in which 200 random teenagers with high
blood pressure will take regular calcium supplements.
a. Assume 0.70 actually is the population proportion that would experience a decrease in
blood pressure. What are the numerical values of the mean and standard deviation of the
sampling distribution of the sample proportions for samples of 200 teenagers?
(
)
70.0
ˆ== pp
µ
( )
(
)
(
)
0324.0
200
30.070.01
ˆ≈=
−
=n
pp
pSD
p
ˆ
.603 .635 .668 .7 .732 .765 .797
b. Use the results of part (a) to calculate an interval that will contain the sample proportion
for about 99.7% of all samples of 200 teenagers.
By the Empirical Rule and part (a) we have (0.603, 0.797).
c. In the clinical trial, 120 of the 200 teenagers taking calcium supplements experienced a
decrease in blood pressure. What is the value of
p
ˆ
for this sample? Is this value a
parameter or a statistic?
60.0
200
120
ˆ==p Statistic.
d. What is the probability of having 120 or fewer experience a decrease of blood pressure
out of a sample of 200 teenagers taking calcium supplements?
normalcdf(-1E99, 0.60, 0.70, 0.0324) = 0.001 or 0.1%
e. We have used the properties of a normal distribution. Show that the
conditions/requirements are satisfied.
1. The selection was an SRS as indicated by “200 random
teenagers.”
2.
10140)7.0(200
≥
=
=
np
3.
(
)
(
)
10603.02001 ≥==− pn
4.
2000)200(1010
=
=
n
There are at least 2000 teenagers with high blood pressure.
