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

ANSWER:

Given that:

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.

Sample Size for 90% CI, E = 0.05 ,

Confidence level = 90% and Desired margin of error, E = 0.05 Minimum Sample Size is given by :

note: Margin of Error = ( Length of CI ) / 2

Best estimate is

Significance level = Confidence = 1 - 0.9 = 0.1

The Critical Value = ( From Z table , using interpolation , 1/2 th distance between 1.64 and 1.65 )

Since the minimum n has to be integer , we take the ceiling of above number and get n = 263

sample Size should be atleast n = 263

Sample Size for 90% CI, E = 0.05 , without

Confidence level = 90% and Desired margin of error, E = 0.05

Since we don't have preliminary estimate we use which requries the maximum n

Significance level Confidence

The Critical value    ( From Z table , using interpolation , 1/2 th distance between 1.64 and 1.65 )

Since the minimum n has to be integer, we take the ceiling of above number and get n = 270

Sample Size should be atleast n = 270