My Math Forum Mean/Std Deviation

 January 26th, 2015, 12:43 PM #1 Newbie   Joined: Jan 2015 From: WI Posts: 8 Thanks: 0 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!
 January 27th, 2015, 12:09 AM #2 Senior Member   Joined: Aug 2012 Posts: 229 Thanks: 3 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).
 January 27th, 2015, 06:37 AM #3 Newbie   Joined: Jan 2015 From: WI Posts: 8 Thanks: 0 Thanks, I think I've got it now!

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