A biologist is interested in constructing a 90% confidence interval for the prop
ID: 2921936 • Letter: A
Question
A biologist is interested in constructing a 90% confidence interval for the proportion of coyotes that survive at least one year after straying from the pack. 42 of the 350 randomly observed coyotes that strayed from the pack were still alive one year later.
A. With 90% confidence the proportion of all coyotes that survive at least one year after straying from the pack is between [ Select ] ["0.072", "0.026", "0.192", "0.091"] and [ Select ] ["0.721", "0.149", "0.156", "0.226"] .
B. If many groups of 350 randomly selected coyotes that strayed from the pack are observed, then a different confidence interval would be produced for each group. About Select ] ["5", "10", "90", "95"] percent of these confidence intervals will contain the true population proportion of all coyotes that survive at least one year after straying from the pack and about [ Select ] ["95", "5", "90", "10"] percent will not contain the true population proportion.
Explanation / Answer
A) here p =42/350 =0.12 and n=350
std error =(p(1-p)/n)1/2 =0.0174
for 90% CI ; z =1.645
therefore 90% confidence interval = p -/+ z*std error =0.091 ; 0.149
hence With 90% confidence the proportion of all coyotes that survive at least one year after straying from the pack is between 0.091 and "0.149"
B) If many groups of 350 randomly selected coyotes that strayed from the pack are observed, then a different confidence interval would be produced for each group. About 90 percent of these confidence intervals will contain the true population proportion of all coyotes that survive at least one year after straying from the pack and about 10 percent will not contain the true population proportion.