Question

Fair Coin? In a series of 100 tosses of a token, the proportion of heads was found to be 0.58. However, the margin of error for the estimate on the proportion of heads in all tosses was too big. Suppose you want an estimate that is in error by no more than 0.05 at the 90% confidence level.

(a) What is the minimum number of tosses required to obtain this type of accuracy? Use the prior sample proportion in your calculation.

You should toss the token at least  times.

(b) What is the minimum number of tosses required to obtain this type of accuracy when you assume no prior knowledge of the sample proportion?

You should toss the token at least  times.

Answer 1

Solution,

Given that,

= 0.58

1 - = 1 - 0.58 = 0.42

margin of error = E = 0.05

At 90% confidence level

= 1 - 90%

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05  = 1.645

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

= (1.645 /0.05 )2 * 0.58 * 0.42

= 263.67

sample size = n = 264

=  1 - =   0.5

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

= (1.645 / 0.05)2 * 0.5 * 0.5

= 270.60

sample size = n = 271