American women is 139 ± 1.4 pounds. (7 points total) a. When asked to interpret this...

American women is 139 ± 1.4 pounds. (7 points total)
a. When asked to interpret this confidence interval, a student says, “95% of all adult
American women would say that their ideal weight is between 137.6 and 140.4
pounds.” Is the student correct? (yes or no) (2 points)
b. Another student interprets the confidence interval this way: “We can be 95%
confident that future samples of adult American women will say that their mean
ideal weight is between 137.6 and 140.4 pounds.” Is this explanation correct? (yes
or no) (2 points)
c. How would you explain what this 95% confidence interval means to these students?
(3 points)
4. Pew Research Center conducted a survey in Greece of 1,010 randomly selected adults.
When asked about immigration, 707 respondents said immigrants are a burden because
they take jobs and social benefits. Pew announces a margin of error of ± 3 percentage
points for all samples of about this size. They also consistently use 95% confidence
intervals. (19 points)
a. What is the actual margin of error (in percent) for the confidence interval for this
sample? (3 points)
b. What would the margin of error have been (as a percentage) if the sample
proportion, ??, was: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, or 0.9 respectively. (Use Excel
to calculate these quickly.) (9 points)
c. Which of the hypothetical sample proportions, ??, from part “b” result in the largest
margin of error? (2 points)
d. Which of the hypothetical sample proportions, ??, from part “b” result in the smallest
margin of error? (2 points)
e. Why do Pew (and other survey organizations) announce a ± 3% margin of error for
all samples about this size? (3 points)