a noted psychic was tested for extrasensory perception (esp). the psychic was presented with 400 cards face…

a noted psychic was tested for extrasensory perception (esp). the psychic was presented with 400 cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, or square. the psychic was correct in 120 cases. let $p$ represent the probability that the psychic correctly identified the symbols on the cards in a random trial.\n\nhow large a sample $n$ would you need to estimate $p$ with margin of error 0.01 and 95% confidence? use the guess $p^{*}=0.25$ as the value for $p$.\n$o n = 7203$\n$o n = 1351$\n$o n = 9604$

a noted psychic was tested for extrasensory perception (esp). the psychic was presented with 400 cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, or square. the psychic was correct in 120 cases. let $p$ represent the probability that the psychic correctly identified the symbols on the cards in a random trial.\n\nhow large a sample $n$ would you need to estimate $p$ with margin of error 0.01 and 95% confidence? use the guess $p^{*}=0.25$ as the value for $p$.\n$o n = 7203$\n$o n = 1351$\n$o n = 9604$

Answer

Explanation:

Step1: Recall sample - size formula

The formula for sample size $n$ in estimating a proportion is $n=\frac{z^{2}\cdot p(1 - p)}{E^{2}}$, where for 95% confidence, $z = 1.96$, $p = 0.25$, and $E=0.01$.

Step2: Substitute values

$n=\frac{(1.96)^{2}\times0.25\times(1 - 0.25)}{(0.01)^{2}}=\frac{3.8416\times0.25\times0.75}{0.0001}=9604$.

Answer:

$n = 9604$