The problem is as follows:
Identify null hypothesis, alternative hypothesis, test statistic, critical value(s) and then make a conclusion about the null hypothesis, and a final conclusion about the original claim.
A song must me no longer than 200 sec. long to be a hit. A simple random sample of 40 songs result in a mean length of 252.5 sec. Assume the population standard deviation of song lengths is 54.5. Use a 0.01 significance level to test the claim that the sample is from a population of songs with a mean greater than 200 sec.
Therefore:
Significance (alpha) = 0.01
Claimed mean (mu) = 200
Population St. Dev. (sigma) = 54.5
Sample size (n) = 40
Sample mean (x bar) = 252.5
I came up with so far:
Null hypothesis: mu = 200 sec.
Alt hypothesis: mu > 200 sec.
Test Statistic z = 6.09
Now I'm running into issues identifying the critical value(s) of z. I came up with critical z plus/minus 2.5758. But when I put that in my homework assignment online, it corrected to 2.33.
I think maybe I'm getting to that point while you're doing homework when everything just sort of jumbles together and you forget how to do what you need to do in order to get the answers. *yawns*
Thanks in advance to anyone that can help me organize my brain, and auto best answer if you can tell me how to do it in StatDisk and not have StatDisk give the wrong critical z.
Identify null hypothesis, alternative hypothesis, test statistic, critical value(s) and then make a conclusion about the null hypothesis, and a final conclusion about the original claim.
A song must me no longer than 200 sec. long to be a hit. A simple random sample of 40 songs result in a mean length of 252.5 sec. Assume the population standard deviation of song lengths is 54.5. Use a 0.01 significance level to test the claim that the sample is from a population of songs with a mean greater than 200 sec.
Therefore:
Significance (alpha) = 0.01
Claimed mean (mu) = 200
Population St. Dev. (sigma) = 54.5
Sample size (n) = 40
Sample mean (x bar) = 252.5
I came up with so far:
Null hypothesis: mu = 200 sec.
Alt hypothesis: mu > 200 sec.
Test Statistic z = 6.09
Now I'm running into issues identifying the critical value(s) of z. I came up with critical z plus/minus 2.5758. But when I put that in my homework assignment online, it corrected to 2.33.
I think maybe I'm getting to that point while you're doing homework when everything just sort of jumbles together and you forget how to do what you need to do in order to get the answers. *yawns*
Thanks in advance to anyone that can help me organize my brain, and auto best answer if you can tell me how to do it in StatDisk and not have StatDisk give the wrong critical z.
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Firstly I'd like to apologise that I don't have access to StatDisk (in fact I don't really know what it is), so I can't help you there.
I'm not really sure how you're working out your critical values, here. Remember you're looking at a standardised distribution when you talk about the "z" value.
So on a distribution table: http://www.chem.uic.edu/tak/chem52409/notes11/tableE_1.gif
When you look for alpha=0.01, you'll see the closest you come to it on this table is 0.0099, and for this value of alpha, z is 2.33.
Alternatively, if you have a GDC, you can opt to use your InvNorm function with an a=0.01, setting your standard deviation to 1 and your mean to 0. This'll give you the near same result of 2.326347...
EDIT: looking back over what you said and the distribution table, it seems like you've halved your significance level somewhere along the line, or something. If this is the case, this may have been where you were going wrong.
I'm not really sure how you're working out your critical values, here. Remember you're looking at a standardised distribution when you talk about the "z" value.
So on a distribution table: http://www.chem.uic.edu/tak/chem52409/notes11/tableE_1.gif
When you look for alpha=0.01, you'll see the closest you come to it on this table is 0.0099, and for this value of alpha, z is 2.33.
Alternatively, if you have a GDC, you can opt to use your InvNorm function with an a=0.01, setting your standard deviation to 1 and your mean to 0. This'll give you the near same result of 2.326347...
EDIT: looking back over what you said and the distribution table, it seems like you've halved your significance level somewhere along the line, or something. If this is the case, this may have been where you were going wrong.