A random sample of size n=100 yielded

p=0.40.

a. Is the sample size large enough to use the large sample approximation to construct a confidence interval forp? Explain.

b. Construct a 90% confidence interval for p.

c. Interpret the 90% confidence interval.

d. Explain what is meant by the phrase "90% confidenceinterval."

a. Is the sample largeenough?

A.

No,becausen

p15andn

q<15.

B.

No,becausen

p<15andn

q15.

C.

No,becausen

p<15andn

q<15.

D.

Yes,becausen

p15andn

q15.

b. The 90% confidence interval for p is (?)

).

(Round to two decimal places asneeded.)

c. Interpret this confidence interval.

A.

We are 90% confident that p lies in the confidence interval.

B.

We are confident that 90% of the population is described by the interval for p.

C.

We are confident that 90% of the population is outside the interval for p.

D.

There is a 90% chance that the value of p is outside the interval.

d. Explain what is meant by the phrase "90% confidenceinterval."

A.

There is a 90% chance that the true value of the parameter is the midpoint of the interval.

B.

The confidence interval is within 10% of the true parameter value.

C.

90% of similarly constructed intervals would be centered on the true value of the parameter.

D.

90% of similarly constructed intervals would contain the true value of the parameter.