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January 26th, 2015, 12:43 PM   #1
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Question Mean/Std Deviation

Hello,
Can anyone help me figure this out?
We want to estimate the mean PCB level in white fish from San Fran Bay. The sample we select has a mean of 642 parts per million and a standard deviation of 54 parts per million. For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean.

Z refers to a variable having a standard normal distribution and t refers to a variable having a t distribution.

1. The sample has size 15, and it is from a population with a distribution about which we know little. Is it Z, t, could use either Z or t, or unclear?

2. The sample has size 110, and it is from a non-normally distributed population. Is it Z, t, either Z or t, or unclear?

3. The sample has size 105, and it is from a non-normally distributed population with a known standard deviation of 52. Is it Z, t, either, or unclear?

4. The sample has size 12, and it is from a normally distributed population with a known standard deviation of 52. Is it Z, t, either, or unclear?

5. The sample has size 13, and it is from a normally distributed population with unknown standard deviation. Is it Z, t, either or unclear?

Thank you!
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January 27th, 2015, 12:09 AM   #2
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Hey ALRS.

Hint: Think of the Central Limit Theorem and consider at what point a t-distribution becomes close enough to a Normal distribution (look at tables or graph for more information).
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January 27th, 2015, 06:37 AM   #3
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Thanks, I think I've got it now!
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