Forty-five percent of primary care doctors think their patients receive unnecessary medical care. If required, round your answer to four decimal places.

(a) Suppose a sample of 300 primary care doctors was taken. Calculate the mean and standad deviation of the sample proportion of doctors who think their patients receive unnecessary medical care.

np =
135

n(1-p) =
165


E( p ) =

=

(b) Suppose a sample of 500 primary care doctors was taken. Calculate the mean and standard deviation of the sample proportion of doctors who think their patients receive unnecessary medical care.

np =
225

n(1-p) =
275


E( p ) =

=

(c) Suppose a sample of 1,000 primary care doctors was taken. Calculate the mean and standard deviation of the sample proportion of doctors who think their patients receive unnecessary medical care.

np =
450

n(1-p) =
550


E( p ) =

=

(d) In which of the preceding three cases, part (a) or part (b) or part (c), is the standard error of p smallest? Why?
The standard error is the smallest in
part (c)
because p is
the same
in parts (a), (b), and (c) and the sample size is largest in
part (c)
.