Question

4. A marketing researcher for a phone company surveys 132 people and finds that the proportion of customers who are likely to switch providers when their contract expires is 18​%.

Complete parts​ a) and​ b) below.

​a) What is the standard deviation of the sampling distribution of the​ proportion? ​(Round to four decimal places as​ needed.)

​b) If she wants to reduce the standard deviation by​ half, how large a sample would she​ need? ​(Round to four decimal places as​ needed.)

Answer 1

a) The standard deviation of the sampling distribution of the proportion here is computed as:

Therefore 0.0334 is the required standard deviation here.

b) The standard deviation is inversely proportional to the square root of sample size, therefore to reduct the standard deviation by half, we need to multiply the sample size by 4 to get here:

New sample size = 132*4 = 528

Therefore 528 is the sample size required here.