A marketing researcher for a phone company surveys 100 people and finds that the

Question

A marketing researcher for a phone company surveys 100 people and finds that the proportion of clients who are likely to switch providers when their contract expires is 0.22. a) What is the estimated standard deviation of the sampling distribution of the proportion? b) If she wants to reduce the estimated standard deviation by half, how large of a sample would she need? a) The estimated standard deviation of the sampling distribution of the proportion is. (Round to four decimal places as needed.)

Explanation / Answer

p = 0.22

n = 100

a) Standard deviation = sqrt(p * (1 - p) / n)

                                   = sqrt(0.22 * (1 - 0.22) / 100)

                                   = 0.0414

b) Standard deviation = sqrt(p * (1 - p) / n)

so, standard deviation is indirectly proportional to sqrt(n)

To reduce the standard deviation by half , we need to increase the sample size by 4 times.

So, the new sample size = 100* 4 = 400

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