This question asks about sampling distributions. There are several urns holding
ID: 3058686 • Letter: T
Question
This question asks about sampling distributions. There are several urns holding different numbers of balls with different combinations of values.
Urn 1 has 24 balls: 8 with value 1, 8 with value 2, and 8 with value 3.
Urn 2 has 24 balls: 8 with value 2, 8 with value 3, and 8 with value 4.
Urn 3 has 90 balls: 30 with value 1, 30 with value 2, and 30 with value 3.
The urns are unlabeled and you want to learn which is which. Imagine taking samples of 5 balls (with replacement) from these urns (n=5) and computing the mean of these samples (sample mean).
How would the distributions of these sample means help you figure which urn is which?
Compare the sample distribution of Urn 1 to Urn 2, Urn 1 to Urn 3, and Urn 2 to Urn 3. You don’t have to compute the actual distributions, just describe them relative to each other (how “peaky”, where centered,…).
How would these distributions (and their relations) change if you increase the sample size to 10?
Finally, would it make any sense to increase the sample size to 30?
Explanation / Answer
This question asks about sampling distributions. There are several urns holding different numbers of balls with different combinations of values.
Urn 1 has 24 balls: 8 with value 1, 8 with value 2, and 8 with value 3.
Urn 2 has 24 balls: 8 with value 2, 8 with value 3, and 8 with value 4.
Urn 3 has 90 balls: 30 with value 1, 30 with value 2, and 30 with value 3.
The urns are unlabeled and you want to learn which is which. Imagine taking samples of 5 balls (with replacement) from these urns (n=5) and computing the mean of these samples (sample mean).
How would the distributions of these sample means help you figure which urn is which?
Compare the sample distribution of Urn 1 to Urn 2, Urn 1 to Urn 3, and Urn 2 to Urn 3. You don’t have to compute the actual distributions, just describe them relative to each other (how “peaky”, where centered,…).
How would these distributions (and their relations) change if you increase the sample size to 10?
Finally, would it make any sense to increase the sample size to 30?
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