Question

What is the probability that a penny I have will land "heads" when tossed? To analyze this question I randomly toss the coin, n=3901 times. On x = 2500 of these tosses, the penny landed "heads." Based upon this sample, I wish to estimate p, the true probability of the penny landing "heads" when tossed. Let p̂ be the sample proportion of "heads" in our sample. Answer the following using R code.

h) Assuming the same p̂ value =0.6409, what sample size would have made the 96% confidence interval for p have a length of .015 or less?

Answer 1

Solution :

Given that,

= 0.6409

1 - = 1-0.6409 = 0.3591

margin of error = E = 0.015

At 96% confidence level

= 1-0.96% =1-0.96 =0.04

/2 =0.04/ 2= 0.02

Z/2 = Z_{0.02 = 2.054}

Z_/2 = 2.054

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (2.054/0.015)² *0.6409*03591

= 4315

sample size = n = 4315