Question

Use the sample data and confidence level given below to complete parts (a) through (d).

A drug is used to help prevent blood clots in certain patients. In clinical trials, among 4144 patients treated with the drug, 124
developed the adverse reaction of nausea. Construct a 99% confidence interval fof the proportion of adverse reactions.
a) Find the best point estimate of the population proportion p.
(Round to three decimal places as needed.)
b) Identify the value of the margin of error E.
E-O
(Round to three decimal places as needed.)
c) Construct the confidence interval
(Round to three decimal places as needed)
d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.
O A. One has 99% confidence that the interval from the lower bound to the upper bound actually does contain the true
value of the population proportion.

Answer 1

Given that,

Sample size,

n

=

4369

Sample proportion,

^

p

=

185

4369

=

0.0423

a)

The sample proportion is a point estimate of the population proportion.

^

p

=

0.0423

b)

The margin of error is defined as:

M

E

=

Z

0.10

/

2

×

√

^

p

(

1

−

^

p

)

n

Excel function for the confidence coefficient:

=NORMINV(0.10/2,0,1)

M

E

=

1.645

×

√

0.0423

(

1

−

0.0423

)

4369

M

E

=

0.005

c)

The 90% confidence interval for the population proportion is defined as:

^

p

±

z

0.10

/

2

√

^

p

(

1

−

^

p

)

n

0.0423

±

1.645

√

0.0423

(

1

−

0.0423

)

4369

(

0.0373

,

0.0473

)