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?
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
= Z0.02 = 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
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