select all distributions which are approximately symmetric.
set a set b
set d set k set i
7. in an experimental study, it was noticed that people who eat more leafy, green vegetables tend to get better sleep than the general population. researchers wonder whether the improved sleep might be caused by the minerals potassium and magnesium found in leafy, green vegetables. how could the researchers design an experiment to determine the effects of potassium and magnesium on sleep?
8. elena is conducting an experiment to determine if high school students are more relaxed when the lights are off or when music is played during an exam. she selects 10 of her friends to take an exam with the lights off and another 10 of her friends to take an exam with music playing. what is problematic about the way that elena selected her groups?
9. an environmental education club has 318 members. select all methods that would select a sample of 20 members at random from the entire environmental education club.
a. ask for 20 members to volunteer to take the survey.
b. place the names of all 318 members on individual slips of paper placed into a bowl. thoroughly mix up the slips and then select 20 of them.
c. number the members from 1 to 318. use a random number generator to make a list of 20 random integers between 1 and 318 inclusive.
d. select 10 of the younger members at random and 10 of the older members at random.
e. send a survey to all 318 members and record the results of the first 20 responses.

Question

select all distributions which are approximately symmetric.
set a set b
set d set k set i
7. in an experimental study, it was noticed that people who eat more leafy, green vegetables tend to get better sleep than the general population. researchers wonder whether the improved sleep might be caused by the minerals potassium and magnesium found in leafy, green vegetables. how could the researchers design an experiment to determine the effects of potassium and magnesium on sleep?
8. elena is conducting an experiment to determine if high school students are more relaxed when the lights are off or when music is played during an exam. she selects 10 of her friends to take an exam with the lights off and another 10 of her friends to take an exam with music playing. what is problematic about the way that elena selected her groups?
9. an environmental education club has 318 members. select all methods that would select a sample of 20 members at random from the entire environmental education club.
 a. ask for 20 members to volunteer to take the survey.
 b. place the names of all 318 members on individual slips of paper placed into a bowl. thoroughly mix up the slips and then select 20 of them.
 c. number the members from 1 to 318. use a random number generator to make a list of 20 random integers between 1 and 318 inclusive.
 d. select 10 of the younger members at random and 10 of the older members at random.
 e. send a survey to all 318 members and record the results of the first 20 responses.

Accepted Answer

### Question 6
# Explanation:
## Step1: Define symmetric distribution
A symmetric distribution has its data mirrored around a central value, with the left half matching the right half of the histogram.
## Step2: Evaluate Set A
Check symmetry: The tallest bar is at 4, with bars on left (1-3) matching right (5-7) in height trend.
## Step3: Evaluate Set B
Check symmetry: The tallest bar is at 6, with bars on left (3-5) matching right (7-9) in height trend.
## Step4: Evaluate Set C
Check symmetry: The tallest bars are at 5-6, with bars on left (2-4) matching right (7-9) in height trend.
## Step5: Evaluate Set D
Check symmetry: Bars are tallest on the left (0-3) and decline right; no mirroring.
## Step6: Evaluate Set E
Check symmetry: Bars are shortest on the left (0-2) and rise right; no mirroring.
## Step7: Evaluate Set F
Check symmetry: Bar heights are inconsistent with no central mirror point.
# Answer:
Set A, Set B, Set C

---

### Question 7
# Brief Explanations:
To isolate the effects of potassium and magnesium, researchers need to control for other variables from leafy greens. They should use a randomized controlled trial with groups that only differ in the intake of these minerals, then measure sleep outcomes.
# Answer:
1. Recruit a large, diverse sample of participants with similar baseline sleep quality.
2. Randomly assign participants to 4 groups:
   - Group 1: Placebo (no potassium/magnesium)
   - Group 2: Potassium supplement only
   - Group 3: Magnesium supplement only
   - Group 4: Both potassium and magnesium supplements
3. Ensure all participants follow identical diets (excluding leafy greens or other high-potassium/magnesium foods) and sleep routines for the study duration.
4. Measure sleep quality (e.g., duration, deep sleep time, wakefulness) using consistent tools (like sleep trackers or surveys) before and during the study.
5. Compare sleep outcomes across the four groups to determine if potassium, magnesium, or their combination improves sleep.

---

### Question 8
# Brief Explanations:
Elena's sample is not representative of the target population (all high school students) and suffers from selection bias, as her friends share similar traits that could affect the results.
# Answer:
1. **Selection Bias**: Elena only selected her friends, which is a convenience sample, not a random sample of all high school students. Her friends may share common characteristics (e.g., similar stress levels, study habits) that could influence their relaxation during exams, making the results ungeneralizable to the broader student population.
2. **Lack of Random Assignment**: She did not randomly assign participants to the two conditions (lights off vs. music playing), which means pre-existing differences between the two friend groups could explain any observed differences in relaxation, rather than the experimental conditions.

---

### Question 9
# Explanation:
## Step1: Define random sampling
Random sampling ensures every member has an equal chance of being selected, with no systematic bias.
## Step2: Evaluate option a
Volunteers are self-selected, not random (bias exists).
## Step3: Evaluate option b
This is a simple random sample (equal chance for all).
## Step4: Evaluate option c
This is a simple random sample (equal chance for all).
## Step5: Evaluate option d
This is stratified sampling, which is a form of random sampling that ensures representation from subgroups.
## Step6: Evaluate option e
First 20 responses are self-selected, not random (bias exists).
# Answer:
b. Place the names of all 318 members on individual slips of paper placed into a bowl. Thoroughly mix up the slips and then select 20 of them.
c. Number the members from 1 to 318. Use a random number generator to make a list of 20 random integers between 1 and 318 inclusive.
d. Select 10 of the younger members at random and 10 of the older members at random.

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QUESTION IMAGE

Question

Explanation:

Question 6

Step1: Define symmetric distribution

Step2: Evaluate Set A

Step3: Evaluate Set B

Step4: Evaluate Set C

Step5: Evaluate Set D

Step6: Evaluate Set E

Step7: Evaluate Set F

Answer:

Question 7