Question

Question Part Points Submissions Used The standard deviation of a sample proportion p̂ gets smaller as the sample size n increases. If the population proportion is p = 0.58, how large a sample is needed to reduce the standard deviation of p̂ to σp hat = 0.004? (The 68−95−99.7 rule then says that about 95% of all samples will have p̂ within 0.01 of the true p. Round your answer to up to the next whole number.)

Answer 1

Answer:

Given,

To determine the n sample

p = 0.58

q = 1 - p

= 1 - 0.58

= 0.42

Now consider,

$\sigma p$ = sqrt($^{^{\sigma 2}}$)

sqrt(pq/n) >= 0.004

substitute the p,q values in the above expression

sqrt(0.58*0.42/n) >= 0.004

n >= 15225