Question

A marketing researcher for a phone company surveys 300 people and finds that the proportion of clients who are likely to switch providers when their contract expires is 0.19. ​a) What is the standard deviation of the sampling distribution of the​ proportion? ​b) If she wants to reduce the standard deviation by​ half, how large of a sample would she​ need? ​a) The standard deviation of the sampling distribution of the proportion is nothing.

Answer 1

Answer:

Given,

p = 0.19

q = 1 - p

= 1 - 0.19

= 0.81

Standard deviation = sqrt(pq/n)

substitute values

= sqrt(0.19*0.81/300)

= 0.0226

Standard deviation = 0.0226

b)

Now if we want to reduce the SD by half then the sample size is given as follows

i.e.,

SD/2 = sqrt(pq/n)

substitute values

0.0226/2 = sqrt(0.19*0.81/n)

0.0113 = sqrt(0.1539/n)

0.00012769 = 0.1539/n

n = 1205.262746

n = 1205