Suppose that X is Normal with u = 10 and that a random sample is taken. This sample is of size n = 5 and has sample mean x = 12 and sample standard deviation s = 3. To find the probability of such a large sample mean occurring, we compute z = 1.49 and find that this sample occurs with probability 0.0681. What is wrong with this computation? (a) The observations do not satisfy the independence assumption. (b) The sample size is too small to use the Normal distribution. (c) We should be computing the left-hand side and thus the probability is 0.9319. (d) We can not use a Normal distribution for this calculation since we do not know o.

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Question  A and B

Suppose that X is Normal with u = 10 and that a random sample is taken. This sample is of size
n = 5 and has sample mean x = 12 and sample standard deviation s = 3. To find the probability
of such a large sample mean occurring, we compute z = 1.49 and find that this sample occurs
with probability 0.0681. What is wrong with this computation?
(a) The observations do not satisfy the independence assumption.
(b) The sample size is too small to use the Normal distribution.
(c) We should be computing the left-hand side and thus the probability is 0.9319.
(d) We can not use a Normal distribution for this calculation since we do not know o.
Transcribed Image Text:Suppose that X is Normal with u = 10 and that a random sample is taken. This sample is of size n = 5 and has sample mean x = 12 and sample standard deviation s = 3. To find the probability of such a large sample mean occurring, we compute z = 1.49 and find that this sample occurs with probability 0.0681. What is wrong with this computation? (a) The observations do not satisfy the independence assumption. (b) The sample size is too small to use the Normal distribution. (c) We should be computing the left-hand side and thus the probability is 0.9319. (d) We can not use a Normal distribution for this calculation since we do not know o.
If the standard deviation of the sample mean is 30, with a sample size of 100, then in order to
reduce the standard deviation of the sample mean to 15, you would need to:
(a) Increase the sample size to 400
(b) Decrease the sample size to 50
(c) Increase the sample size to 200
(d) Change the population standard deviation to o = 150.
Transcribed Image Text:If the standard deviation of the sample mean is 30, with a sample size of 100, then in order to reduce the standard deviation of the sample mean to 15, you would need to: (a) Increase the sample size to 400 (b) Decrease the sample size to 50 (c) Increase the sample size to 200 (d) Change the population standard deviation to o = 150.
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