SOLUTION: 2.A doctor claims that about 30 percent of all persons exposed to a certain amount of radiation will feel any ill effects. Among 19 randomly selected samples who were exposed to ra

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Question 1199897: 2.A doctor claims that about 30 percent of all persons exposed to a certain amount of radiation will feel any ill effects. Among 19 randomly selected samples who were exposed to radiation, only 1 felt any ill effects.
A.Construct the 95% confidence interval for the population proportion?
B.Test whether the proportion of population who are exposed to radiation fell any ill effect is less than doctor’s claim α = .05 level of significance?
test the null hypothesis θ = 0.30 against the alternative hypothesis θ < 0.30 at the α = .05 significance level
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
claim is population p = 30%
sample size is 19.
sample p = 1/19 = .0526 * 100 = 5.26%
test is whether actual percent is less than 30.
standard error equals (30 * 70 / 19) = 10.5
z = (5.26 - 30) / 10.5 = -2.36
critical z at .95 one sided confidence interval is -1.65.
test z is greater than critical z, so test results are significant.
conclusion is that the percent of all persons exposed to a certain amount of radiation is less than 30%.