Question

You are interested in constructing a 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 379 randomly selected caterpillars observed, 47 lived to become butterflies. Round answers to 4 decimal places where possible. a. With 90% confidence the proportion of all caterpillars that lived to become a butterfly is between and b. If many groups of 379 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion. Hint: Hints Video [+]

Answer 1

a)

sample success x =		47
sample size          n=		379
sample proportion p̂ =x/n=		0.12401
std error se= √(p*(1-p)/n) =		0.0169
for 90 % CI value of z=		1.645
margin of error E=z*std error   =		0.028
lower bound=p̂ -E                       =		0.0962
Upper bound=p̂ +E                     =		0.1519

...is between 0.0962 and 0.1519

(please try 0.0962 and 0.1518 if this comes wrong)

b)

about 90 percent of these confidence intervals will contain..........and about 10 percent will not contain.............