Quiz 8.2A
AP Statistics
Name:
1. A simple random sample of 1100 males aged 12 to 17 in the United States were asked
whether they played massive multiplayer online role-playing games (MMORPGs); 775 said
that they did. We want to use this information to construct a 95% confidence interval to
estimate the proportion of all U.S. males aged 12 to 17 who play MMORPGs.
(a) State the parameter our confidence interval will estimate.
the proportion of all us males aged 12 to 17 who play mmorpgs
(b) Identify each of the conditions that must be met to use this procedure, and explain how
you know that each one has been satisfied.
randomization: SRS was taken
Independence: 1100 is less than 10% of the population.
(c) Find the appropriate critical value and the standard error of the sample proportion.
z=1.94
se=0.014
(d) Give the 95% confidence interval.
0.655, 0.755
(e) Interpret the confidence interval constructed in part (d) in the context of the problem.
we are 95% confident that the interval from 0.655 to 0.755 contains the true
proportion of males aged 12 to 17 who play mmorpgs
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(f) Suppose you wanted to estimate the proportion of 12-to-17 year-old males who play
MMORPG’s with 95% confidence to within ± 2%. Calculate how large a sample you
would need.
1998
(g) If you wanted to have a margin of error of ±2% with 99% confidence, would your sample
have to be larger, smaller, or the same size as the sample in part (f)? Explain.
larger, increasing the sample size reduces variability which increase
confidence in the interval’s ability to capture the parameter
(h) This poll was conducted through email. Explain how undercoverage could lead to a
biased estimate in this case, and speculate about the direction of the bias.
a poll given through email will undercover these in the population who spend less time online or not
online at all. this will cause the sample to overestimate the population of males who play mmorpgs
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Quiz 8.2B
AP Statistics
Name:
1. A recent poll found that “433 of the 1548 randomly-selected adults questioned felt that
unemployment compensation should be extended an additional six months while the country
is in it current economic downturn.” We want to use this information to construct a 95%
confidence interval to estimate the proportion of the U.S. adults who feel this way.
(a) State the parameter our confidence interval will estimate.
(b) Identify each of the conditions that must be met to use this procedure, and explain how
you know that each one has been satisfied.
(c) Find the appropriate critical value and the standard error of the sample proportion.
(d) Give the 95% confidence interval.
(e) Interpret the confidence interval constructed in part (d) in the context of the problem.
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(f) Suppose you wanted to estimate the proportion of people who feel that unemployment
compensation should be expanded with 95% confidence to within ± 1.5%. Calculate how
large a sample you would need.
(g) If you wanted to have a margin of error of ±1.5% with 99% confidence, would your
sample have to be larger, smaller, or the same size as the sample in part (f)? Explain.
(h) This poll was conducted by randomly calling cell phone numbers. Explain how
undercoverage could lead to a biased estimate in this case, and speculate about the
direction of bias.
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