Winter Olympics (Example 12) According to a 2018 Rasmussen Poll, 40 % of American adults were very likely to watch some of the Winter Olympic coverage on television. The survey polled 1000 American adults and had a margin of error of plus or minus 3 percentage points with a 95 % level of confidence. a. State the survey results in confidence interval form and interpret the interval. b. If the Rasmussen Poll was to conduct 100 such surveys of 1000 American adults, how many of them would result in confidence intervals that included the true population proportion? c. Suppose a student wrote this interpretation of the confidence interval: “We are 95 % confident that the sample proportion is between 37 % and 43 % . ” What, if anything, is incorrect in this interpretation?
Winter Olympics (Example 12) According to a 2018 Rasmussen Poll, 40 % of American adults were very likely to watch some of the Winter Olympic coverage on television. The survey polled 1000 American adults and had a margin of error of plus or minus 3 percentage points with a 95 % level of confidence. a. State the survey results in confidence interval form and interpret the interval. b. If the Rasmussen Poll was to conduct 100 such surveys of 1000 American adults, how many of them would result in confidence intervals that included the true population proportion? c. Suppose a student wrote this interpretation of the confidence interval: “We are 95 % confident that the sample proportion is between 37 % and 43 % . ” What, if anything, is incorrect in this interpretation?
Solution Summary: The author explains how the 95 % confidence interval for the population proportion is calculated.
Winter Olympics (Example 12) According to a 2018 Rasmussen Poll,
40
%
of American adults were very likely to watch some of the Winter Olympic coverage on television. The survey polled 1000 American adults and had a margin of error of plus or minus 3 percentage points with a
95
%
level of confidence.
a. State the survey results in confidence interval form and interpret the interval.
b. If the Rasmussen Poll was to conduct 100 such surveys of 1000 American adults, how many of them would result in confidence intervals that included the true population proportion?
c. Suppose a student wrote this interpretation of the confidence interval: “We are
95
%
confident that the sample proportion is between
37
%
and
43
%
.
”
What, if anything, is incorrect in this interpretation?
During busy political seasons, many opinion polls are conducted. In apresidential race, how do you think the participants in polls are generally selected?Discuss any issues regarding simple random, stratified, systematic, cluster, andconvenience sampling in these polls. What about other types of polls, besides political?
Please could you explain why 0.5 was added to each upper limpit of the intervals.Thanks
28. (a) Under what conditions do we say that two random variables X and Y are
independent?
(b) Demonstrate that if X and Y are independent, then it follows that E(XY) =
E(X)E(Y);
(e) Show by a counter example that the converse of (ii) is not necessarily true.
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