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

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Statistics

Wildlife biologists inspect 150 deer taken by hunters and find26 of them carrying ticks that test positive for Lyme disease.

a.) Create a​ 90% confidence interval for the percentage of deerthat 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?

Answer & Explanation Solved by verified expert
4.1 Ratings (845 Votes)

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
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