SOLUTION: An educator estimates that the dropout rate for seniors at high schools in Colorado is 12%. Last year in a random sample of 300 Colorado seniors, 27 withdrew from school. At α = 0

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Question 1178602: An educator estimates that the dropout rate for seniors at high schools in Colorado is 12%. Last year in a random sample of 300 Colorado seniors, 27 withdrew from school. At α = 0.05, is there enough evidence to reject the educator’s claim?
Found 2 solutions by Boreal, ewatrrr:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
point estimate is 9%
Ho: p=0.12
Ha: p NE 0.12
alpha = 0.05 p{reject Ho|Ho true}
test stat is a z=(p hat-p)/sqrt(p(1-p)/n)
two way test, reject z if |z|>1.96
z=-0.03/sqrt(.12*.88/300)
=-0.03/0.0188
=-1.60
fail to reject Ho, insufficient evidence to refute educator's claim.
p-value is 0.11

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
population:  p = .12 
sample:  n = 300   x̄ = 27/300 = .09
Ho:  p = .12
Ha:  p < .12
a=0.05, one-tailed: z(.95) = 1.645 critical value

 z = -1.6
|-1.6| < 1.645
Fail to Reject Ho, Insufficient evidence
Wish You the Best in your Studies.