answer whether you think the central limit theorem applies to each of the following situations. if it does apply, specify the population of interest and the measurement of interest. if it does not apply, explain why not.
(a) a researcher is interested in what the average cholesterol level would be if people restricted their fat intake to 30% of calories. he gets a group of 87 patients who have had heart - attacks to volunteer to participate, puts them on a restricted diet for a few months, and then measures their cholesterol.
- the theorem applies. the population is cholesterol level and the measurement is heart - attack patients.
- the theorem applies. the population is people in general and the measurement is fat intake.
- the theorem does not apply because the sample is not random.
- the theorem does not apply because the measurement is not bell - shaped and the sample is not large enough.
(b) a large corporation would like to know the average income of the spouses of its workers. rather than go to the trouble to collect a random sample, they post someone at the exit of the building at 5 p.m. everyone who leaves between 5 p.m. and 5:30 p.m. is asked to complete a short questionnaire on the issue. there are 79 responses.
- the theorem applies. the population is spouses of workers at a corporation and the measurement is income of the spouses.
- the theorem applies. the population is spouses of workers at a corporation and the measurement is combined income of both spouses.
- the theorem does not apply because the sample is not random.
- the theorem does not apply because the measurement is not bell - shaped and the sample is not large enough.

Question

answer whether you think the central limit theorem applies to each of the following situations. if it does apply, specify the population of interest and the measurement of interest. if it does not apply, explain why not.
(a) a researcher is interested in what the average cholesterol level would be if people restricted their fat intake to 30% of calories. he gets a group of 87 patients who have had heart - attacks to volunteer to participate, puts them on a restricted diet for a few months, and then measures their cholesterol.
  - the theorem applies. the population is cholesterol level and the measurement is heart - attack patients.
  - the theorem applies. the population is people in general and the measurement is fat intake.
  - the theorem does not apply because the sample is not random.
  - the theorem does not apply because the measurement is not bell - shaped and the sample is not large enough.
(b) a large corporation would like to know the average income of the spouses of its workers. rather than go to the trouble to collect a random sample, they post someone at the exit of the building at 5 p.m. everyone who leaves between 5 p.m. and 5:30 p.m. is asked to complete a short questionnaire on the issue. there are 79 responses.
  - the theorem applies. the population is spouses of workers at a corporation and the measurement is income of the spouses.
  - the theorem applies. the population is spouses of workers at a corporation and the measurement is combined income of both spouses.
  - the theorem does not apply because the sample is not random.
  - the theorem does not apply because the measurement is not bell - shaped and the sample is not large enough.

Accepted Answer

# Brief Explanations:
- (a) The Central Limit Theorem requires a random sample. Here, the sample consists of heart - attack patients who volunteer, which is not a random sample of the general population. So the theorem does not apply.
- (b) To use the Central Limit Theorem, the sample should be random. In this case, employees leaving between 5 p.m. and 5:30 p.m. are surveyed, which is not a random sample of all spouses of workers. So the theorem does not apply.
# Answer:
- (a) The theorem does not apply because the sample is not random.
- (b) The theorem does not apply because the sample is not random.

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