Estimating Sample Size In the 2018 study Closing the STEM Gap, researchers wanted to estimate the percentage of middle school girls who planned to major in a STEM field. a. If a 95 % confidence level is used, how many people should be included in the survey if the researchers wanted to have a margin of error of 3 % ? b. How could the researchers adjust their margin of error if they want to decrease the number of study participants?
Estimating Sample Size In the 2018 study Closing the STEM Gap, researchers wanted to estimate the percentage of middle school girls who planned to major in a STEM field. a. If a 95 % confidence level is used, how many people should be included in the survey if the researchers wanted to have a margin of error of 3 % ? b. How could the researchers adjust their margin of error if they want to decrease the number of study participants?
Solution Summary: The author explains the relationship between the margin of error and the sample size.
Estimating Sample Size In the 2018 study Closing the STEM Gap, researchers wanted to estimate the percentage of middle school girls who planned to major in a STEM field.
a. If a
95
%
confidence level is used, how many people should be included in the survey if the researchers wanted to have a margin of error of
3
%
?
b. How could the researchers adjust their margin of error if they want to decrease the number of study participants?
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
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.
Elementary Statistics: Picturing the World (7th Edition)
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