Explain who is using the better method and why?

Question

Mr smith and mr. Jones both plan to do an experiment to determine whether a coin (would land heads 50% of the time) Mr. Smith plans to flip the coin 1,000 times, but Mr. Jones only plans to flip it 10 times. Explain who is using the better method and why? 

Answer 1

1 thousand flips better than 10 flips

the bigger the sample the more reliable the estimated mean

the smaller the variance and standard deviation

the smaller the CI

for A

mean = np = 1000x.5 = 500. 500/1,000 = 1/2

variance = npq =1000x.5x.5 = 250

standard deviation = sqr250 = 5sqr10

for B

mean = np = 10x.5 = 5. 5/10 = 1/2

variance = npq = .5x.5 = 1/4

sd = sqr(1/4) = 1/2

68% of the time A will get a sample mean in the interval (1/2+/-5sqr10)

68% of the B gets mean in (1/2 +/-1/2)