Question

A psychic was tested for ESP. The psychic was presented with 400 cards face down and was asked to determine if the card was one of four symbols: a cross, a star, a circle, or a square. The psychic was correct in 120 of the cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial.

Using the results above, construct a 99% confidence interval for p.

Answer 1

Use a confidence interval formula for proportions.

Here's one example:
CI99 = p + or - (2.58)(sqrt of pq/n)
...where sqrt = square root, p = x/n, q = 1 - p, and n = sample size.

p = 120/400
q = 280/400
n = 400

Convert all fractions to decimals before using the formula to plug in the numbers.

I'll let you take it from here.