Question

Fair Coin? In a series of 100 tosses of a token, the proportion of heads was found to be 0.61. 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 0.04 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

a)

The following information is provided,
Significance Level, α = 0.1, Margin or Error, E = 0.04, σ = 0.61

The critical value for significance level, α = 0.1 is 1.645.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (1.645 * 0.61/0.04)^2
n = 629.32

Therefore, the sample size needed to satisfy the condition n >= 629.32 and it must be an integer number, we conclude that the minimum required sample size is n = 630
Ans : Sample size, n = 630 or 629

b)
The following information is provided,
Significance Level, α = 0.1, Margin or Error, E = 0.04, σ = 0.5

The critical value for significance level, α = 0.1 is 1.645.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (1.645 * 0.5/0.04)^2
n = 422.82

Therefore, the sample size needed to satisfy the condition n >= 422.82 and it must be an integer number, we conclude that the minimum required sample size is n = 423
Ans : Sample size, n = 423 or 422