According to a recent article, 58% of Americans (aged 18 or older) disapprove of the job the
Supreme Court is doing. (If you are interested: Supreme Court Trust, Job Approval at Historical
Lows (gallup.com)) Results for this Gallup poll are based on telephone interviews conducted
Sept. 1-16, 2022, with a random sample of 812 adults, aged 18 and older, living in all 50 U.S.
states and the District of Columbia.)
1. If you took a random sample of 20 people, how many would you expect to
disapprove of the job the Supreme Court is doing?
2. If you took a random sample of 20 people, what is the probability that more
than 15 disapprove of the job the Supreme Court is doing?
3. If you took a random sample of 20 people, what is the probability that no more
than 10 disapprove of the job the Supreme Court is doing?
4. Are the conditions met to create a confidence interval for this proportion?
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5.Regardless of your answer to Part 3, what is the 95% confidence interval for
this survey? Make sure you interpret your results in a sentence.
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6. What sample size should the researchers use if they perform the survey
again next year and want to be within 3 percentage points if
a. They use this year's estimate
b.
They don't use a prior estimate