Question

In: Statistics and Probability

Your book describes the normal curve as a “theoretical distribution”. What do the authors mean by...

  1. Your book describes the normal curve as a “theoretical distribution”. What do the authors mean by this?
  2. Using the textbook and lecture, to the best of your ability tell me what a sampling distribution is, and what is it used for.
  3. Using your textbook and lecture, what do we call the standard deviation of the sampling distribution? Why is it important (hint: the text book is only ok on this, though I discuss it in the lecture several times).
  4. Using your textbook and lecture, what does the central limit theorem tell us in practical terms?
  5. To the best of your ability, answer the following questions about the New York Times Inference Video:
    1. If the researcher collected information on ALL the rabbits in the forest, what would we call that? Why can’t he do it?
    2. If he measures many small groups and takes their averages, what is he making? (the averages of samples – what the heck is that in our statistical language!?)
    3. What happens to the distribution of averages when he adds more rabbits to his samples?
    4. What is the point they are trying to make about the distribution of dragon wing spans that is relevant to our discussion of inference?
    5. Why is having a large number of rabbits or dragons in your sample so important?

Solutions

Expert Solution

(a)

Question:

If the researcher collected information on ALL the rabbits in the forest, what would we call that? Why can’t he do it ?

If the researcher collected information on ALL the rabbits in the forest, we would call that complete enumeration or census method. He can't do it because collecting information on ALL the rabbits in the forest is not at all practicable.

(b)

Question:

If he measures many small groups and takes their averages, what is he making? (the averages of samples – what the heck is that in our statistical language!?)

If he measures many small groups and takes their averages, he is making Sampling Distribution of Sample Means.

(c)

Question:

What happens to the distribution of averages when he adds more rabbits to his samples?

When he adds more rabbits to his samples, the sample size becomes large and by Central Limit Theorem, the distribution of averages tends to Normal Distribution.

(d)

Question:

What is the point they are trying to make about the distribution of dragon wing spans that is relevant to our discussion of inference?

The distribution of dragon wing spans tends to normal distribution and thus our prediction becomes more reliable as the sample size becomes large.

(e)

Question:

Why is having a large number of rabbits or dragons in your sample so important?

Having a large number of rabbits or dragons in your sample is so important because only when the sample size = n >30, Large Sample, Central Limit Theorem is applicable and only in that case the sampling distribution of sample means tends to normal distribution making our predictions more reliable.


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