1.In a survey conducted by the Pew Research Center in 2010 41% of Americans supp
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Question
1.In a survey conducted by the Pew Research Center in 2010 41% of Americans support the legalization of marijuana in the U.S. The researchers note that the margin of error is ± 3% using 95% confidence.
What does this margin of error tell you about the results of the survey?
A. We are 95% confident that the results are off by 3%.
B. 3% of the respondents gave a fake answer.
C.We can be 95% confident that the proportion of all Americans who support legalization of marijuana is within 3% of 41%.
D.We are certain that the proportion of all Americans who support legalization of marijuana is between 38% and 44%.
2. Privacy issues: In a Fall 2014 Pew Research survey, 25% of American adults say they are “not at all confident” that the records of their activity maintained by credit card companies will remain private and secure. With numerous data breaches since then, a consumer group is interested in determining whether the proportion has increased this year. They select a random sample of 300 adults and find that 30% state they are not at all confident.
After conducting the hypothesis test for p = 0.25 compared to p > 0.25, we obtain a P?value of 0.023. Which of the following interpretations of the P?value is correct?
A.There is a 2.3% chance that 25% of American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure.
B.There is a 2.3% chance that 30% of American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure.
C.There is a 2.3% chance that 30% or more of American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure if we assume 25% of American adults are not at all confident in 2014.
D.There is a 2.3% chance that 30% or more of a sample of 300 American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure if 25% of Americans are not at all confident this year.
3. In a study of a new treatment for cold sores, researchers randomly assigned 2209 patients to use of the new topical medication or a placebo in a double-blind experiment. Cold sores healed more quickly with the new medication and the improvement was statistically significant at the 0.01 level. Results were published the Journal of the American Medical Association in 1997. (http://jama.jamanetwork.com/article.aspx?articleid=415844)
Which of the following is an appropriate conclusion?
A.With a large sample, statistically significant results suggest a large improvement over the placebo.
B.With a large sample, statistically significant results may come from a small improvement over the placebo.
C.Regardless of the sample size, a statistically significant result means there is a meaningful difference in cold sore relief.
Explanation / Answer
Result:
1.In a survey conducted by the Pew Research Center in 2010 41% of Americans support the legalization of marijuana in the U.S. The researchers note that the margin of error is ± 3% using 95% confidence.
What does this margin of error tell you about the results of the survey?
A. We are 95% confident that the results are off by 3%.
B. 3% of the respondents gave a fake answer.
C.We can be 95% confident that the proportion of all Americans who support legalization of marijuana is within 3% of 41%.
Answer: D.We are certain that the proportion of all Americans who support legalization of marijuana is between 38% and 44%.
( we are 95% that true proportion will fall between lower limit and upper limit.)
2. Privacy issues: In a Fall 2014 Pew Research survey, 25% of American adults say they are “not at all confident” that the records of their activity maintained by credit card companies will remain private and secure. With numerous data breaches since then, a consumer group is interested in determining whether the proportion has increased this year. They select a random sample of 300 adults and find that 30% state they are not at all confident.
After conducting the hypothesis test for p = 0.25 compared to p > 0.25, we obtain a P?value of 0.023. Which of the following interpretations of the P?value is correct?
A.There is a 2.3% chance that 25% of American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure.
B.There is a 2.3% chance that 30% of American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure.
C.There is a 2.3% chance that 30% or more of American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure if we assume 25% of American adults are not at all confident in 2014.
Answer: D.There is a 2.3% chance that 30% or more of a sample of 300 American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure if 25% of Americans are not at all confident this year.
3. In a study of a new treatment for cold sores, researchers randomly assigned 2209 patients to use of the new topical medication or a placebo in a double-blind experiment. Cold sores healed more quickly with the new medication and the improvement was statistically significant at the 0.01 level. Results were published the Journal of the American Medical Association in 1997. (http://jama.jamanetwork.com/article.aspx?articleid=415844)
Which of the following is an appropriate conclusion?
A.With a large sample, statistically significant results suggest a large improvement over the placebo.
B.With a large sample, statistically significant results may come from a small improvement over the placebo.
Answer: C.Regardless of the sample size, a statistically significant result means there is a meaningful difference in cold sore relief.
( if the sample is representative, regardless of sample size ,then there is meaningful difference.)
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