Wildlife biologists inspect 150 deer taken by hunters and find 26 of them carrying ticks that...

Wildlife biologists inspect 150 deer taken by hunters and find 26 of them carrying ticks that test positive for Lyme disease.

a.) Create a 90% confidence interval for the percentage of deer that may carry such ticks.( __%,__%)

b.) If the scientists want to cut the margin of error in half, how many deer must they inspect?

c.) What concerns do you have about this sample?

Expert Solution

sample success x =	26
sample size n=	150
sample proportion p̂ =x/n=	0.1730

std error se= √(p*(1-p)/n) =	0.0309

for 90 % CI value of z=	1.645
margin of error E=z*std error =	0.0508
lower bound=p̂ -E =	0.1222
Upper bound=p̂ +E =	0.2238
from above 90% confidence interval for population proportion =12.22% , 22.38 %

b)

since margin of error is inversly proportion to square root of sample size

therefore required sample size =4*150 =600

c)

since above is a sample of deer taken by hunters , this might not represent the population of deer in focus and may give biased results

orchestra answered 1 year ago

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