Question

Not all hospitals can afford to have an Obstetrics wards due to cost consideration. It is known that in City and Regional areas, 20% of hospitals have an Obstetrics wards. Among the health professionals, there is serious concern that the proportion of hospitals with Obstetrics wards is much lower in the Rural area than the City or Regional areas. Assume that the data is a random sample of all hospitals in Australia.

Obstetrics Ward * Region of Hospital
Count
		Region of Hospital			Total
		City	Regional	Rural
Obstetrics Ward	Yes	8	15	14	37
	No	8	9	105	122
Total		16	24	119	159

(f) If a health professional wants to be 95% confident that the margin of error of the estimate of the true proportion of rural hospitals with obstetrics wards in Australia is within 0.06, what minimum sample size is required? For calculations, use an estimated proportion from the given data.

(g) If the health professional decides to use a conservative method (approach), what will be the minimum sample size to keep the same level of confidence and margin of error as in part (f)? What is the impact of this decision? (Include evidence to support your answer).

Answer 1

(f)

Minimum Sample Size (n) is given by:

Given:

= 0.05

From Table, critical values of Z = 1.96

p = 0.20

e = 0.06

Substituting, we get:

So,

Answer is:

171

(g)

For conservative method (approach), take p = 0.5.

Substituting, we get:

So,

Answer is:

267

The impact of this decision is that the minimum sample size has increased from 171 to 267.