Question

A hat contain 100,000 balls. A random sample of 400 balls is selected from the hat. 58 balls in the sample are red, 257 balls in sample are brown, and the rest of the balls in the sample are yellow. At a 5% significant level, use the p-value method to test the claim that the 25% of balls in the hat are yellow.

Answer 1

H0 : p = 0.25
ha: p not equasl to 0.25

test statistics:

phat = 85/400 =0.2125

z = (phat - p)/sqrt(p*(1-p)/n)
= (0.2125 - 0.25)/sqrt(0.25*(1-0.25)/400)
= -1.73

p value = 0.0833

Do not reject H0 as p value > 0.05