Question

A marketing researcher for a phone company surveys 130 people and finds that the proportion of customers who are likely to switch providers when their contract expires is 12​%. Complete parts​ a) and​ b) below. ​a) What is the standard deviation of the sampling distribution of the​ proportion? SD (ModifyingAbove p with caret )equals nothing ​(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? nequals nothing ​(Type a whole​ number.)

Answer 1

σ = 0.0285 ;

n = 520

Explanation:

Sample size, n = 130

p = 0.12

q = 1 - 0.12 = 0.88

σ = sqrt(pq/n)

σ = sqrt[(0.12 * 0.88) / 130]

σ = sqrt(0.0008123)

σ = 0.0285010

σ = 0.0285

If σ is reduced by half

0.0285 / 2 = sqrt(0.1056 / n)

0.01425 = sqrt(0.1056 / n)

Square both sides

0.0002030625 = 0.1056 / n

n = 0.1056 / 0.0002030625

n = 520.03693

n = 520