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22:48, 27/01/2026
Estimating Population Proportions: Confidence Intervals & Analysis - Studocu
1. You play a game and win 136 out of 270 times.
o Estimate the probability of winning the game.
o Find a 95% confidence interval for the probability of winning the game.
2. Find zα/2 for a 90% confidence interval for a proportion.
3. A CBS News/New York Times poll found that 329 out of 763 adults said
they would travel to outer space in their lifetime, given the chance.
Estimate the true proportion of adults who would like to travel to outer space with 92% confidence.
4. The Gallup Poll found that 27% of adults surveyed nationwide said they
had personally been in a tornado. How many adults should be surveyed to
estimate the true proportion of adults who have been in a tornado with a
95% confidence interval 5% wide?
5. A recent study indicated that 29% of the 100 women over age 55 in the study were widows.
o Find a 90% confidence interval for the true proportion of women over age 55 who are widows.
o How large a sample must one take to be 90% confident that the
estimate is within 0.05 of the true proportion of women over age 55 who are widows?
o If no estimate of the sample proportion is available, how large
should the sample be to be 90% confident that the estimate is
within 0.05 of the true proportion?
6. An organization advertises that on a given poll, 43% answered "yes" to
the question "Would you rather have a boring job than no job?", with a
margin of error of ±1%. What did the organization fail to reveal?
7. Upon taking a sample to estimate a population proportion, why is it better
to report a confidence interval than pˆ, the best point-estimate for this proportion.? 22:48, 27/01/2026
Estimating Population Proportions: Confidence Intervals & Analysis - Studocu
1. Express the confidence interval 0.200

form of pˆ±E
2. Find the confidence interval for a proportion if p^=0.222 and the margin of error is 0.044.
3. If a sample is used to estimate a population proportion pp, find the
margin of error E that corresponds to n=1000,x=400, and 95% confidence.
4. Construct a 95% confidence interval to estimate a population proportion p if n=200,x=40.
5. Construct a 99% confidence interval for a population proportion p if n=1236,x=109
6. What sample size should be used to estimate a population proportion
within 0.045 with 95% confidence?
7. What sample size should be used to estimate a population proportion
within 2%, with 99% confidence, when a prior study estimated p^=0.14?
8. A medication is suspected of increasing the likelihood of conceiving a
girl. Of 574 pregnancies where the mother was taking this medication
during her pregancy, 525 of them gave birth to a girl. Construct
a 95% confidence interval for the proportion of births that result in a girl
when the mother is taking this medication.
9. In one of Mendel's famous genetics experiments with peas, he predicted
that 25% of offspring peas would be yellow. He instead saw 152 yellow
peas and 428 green peas. Find a 95% confidence interval estimate for the
percentage of yellow peas. Do the results contradict his hypothesis?
10.In a study of 420,095 cell phone users, 135 developed brain cancer or
cancer of the nervous system. Prior to this study, it was found that the rate
of such cancers was 0.034% for people not using cell phones. Construct
a 95% confidence interval for the proportion of cell phone users that 22:48, 27/01/2026
Estimating Population Proportions: Confidence Intervals & Analysis - Studocu
develop such cancers. Is there a significant difference between cell phone
users and people that don't use cell phones?
11.Assuming we wish to estimate the proportion of American adults who use
the internet within 2% and be 99% confident in our results, how many
randomly selected adults should we survey? 22:48, 27/01/2026
Estimating Population Proportions: Confidence Intervals & Analysis - Studocu