When members of a philanthropic organization send out a fundraising letter, they

Question

When members of a philanthropic organization send out a fundraising letter, they get a return from about 6% of the people on their mailing list. They simulated 1000 mailings for samples of size n with success rate p 0.06. The sample statistics from each simulation are shown in the table. Complete parts (a) through (d) below 20 50 100 200 mean 0.0607 0.0594 0.0596 0.0598 standard dev 0.0525 0.0335 0.0236 0.0169 Click the icon to view histograms of the simulations. a) According to the Normal model, what should the theoretical mean and standard deviations be for these sample sizes? Complete the following table theoretical mean theoretical standard deviation 20 50 100 200 (Round to four decimal places as needed.) b) How close are those theoretical values to what was observed in these simulations? Select the correct choice below and, if necessary, fill in any answer boxes within your choice O A. While of the 8 theoretical values are very close to the observed values, the remaining are not. O B. All of the theoretical values are very close to the observed values O C. None of the theoretical values are very close to the observed values. c) Looking at the histograms, at what sample size would you be comfortable using the Normal model as an approximation for the sampling distribution? Select the correct choice below and fill in the answer box within your choice

Explanation / Answer

for theoritical mean p=0.06

and std deviation =(p*(1-p)/n)1/2

a)

b)

option B is correct

c)

option A ; sample size 200

d)

option D

n theoritical mean theoritical std deviaiton 20 0.06 0.0531 50 0.06 0.0336 100 0.06 0.0237 200 0.06 0.0168

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