1. Over half of all American teens (ages 12 to 17 years) have an
online profile, mainly on Facebook. A random sample of 465 teens
with profiles found that 282 included photos of themselves.
(a) Give the 96% large-sample confidence interval for the
proportion p of all teens with profiles who include photos
Large-sample Interval: to
(b) Give the plus four 96% confidence interval for p .
(The plus-four interval always pulls the results away from 0% or
100%, whichever is closer. Even though the condition for using the
large-sample interval is met, the plus four interval is more
Plus four Interval: to
2. Some shrubs have the useful ability to resprout from their
roots after their tops are destroyed. Fire is a particular threat
to shrubs in dry climates, as it can injure the roots as well as
destroy the aboveground material. One study of resprouting took
place in a dry area of Mexico. The investigation clipped the tops
of samples of several species of shrubs. In some cases, they also
applied a propane torch to the stumps to simulate a fire. Of 12
specimens of a particular species, 7 resprouted after fire.
Estimate with 90% confidence the proportion of all shrubs of this
species that will resprout after fire.
Interval: ____to _____
A Gallup poll asked a sample of Canadian adults if they thought
the law should allow doctors to end the life of a patient who is in
great pain and near death if the patient makes a request in
writing. The poll included 275 people in Quebec, 191 of whom agreed
that doctor-assisted suicide should be allowed.
(a) What is the margin of error of the large-sample 90%
confidence interval for the proportion of all Quebec adults who
would allow doctor-assisted suicide?
(b) How large a sample is needed to get aÂ±3 percentage point
margin of error (this is very commonly used)? Use the previous
sample as a pilot study to get p*. (You may need four decimal
places in your critical value to solve this problem.)