The examples with * are adapted from: Triola, Mario F. Elementary statistics. Boston, Mass: Addison-Wesley, 2001. Print.
1. *Is the temperature of the average human body actually 98.6?
x-bar=98.2, sd=0.62, n=106
sd vs sigma -- why does it matter?
it doesn't if n>30
2. Subway footlong subs: re we getting a full footlong sandwich?
x-bar=11.89 inches, sigma=.92, n=130
3. *NyQuil is supposed to contain (15 mg/15 mL) of Dextromethorphan. Does the content of the actual medicine match our expectations?
x-bar=15.22 mg, sigma=1.13, n=88
4. *"Forty people are selected and the accuracy of their wristwatches are checked." Positive times are ahead; negative times are behind. Can we say that the average watch is on time? All measurements are in seconds.
x-bar=117.3, sd=185, n=40
5. *A vitamin supplement is given to mothers of male babies. We are checking to see if it has an effect on the birth weight.
3.73, 4.37, 3.73, 4.33, 3.39, 3.68, 4.68, 3.52, 3.02, 4.09, 2.47, 4.13, 4.47, 3.22, 3.43, 2.54
mu (all male babies) = 3.39
n<30 ... uh oh.
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https://infocus.emc.com/william_schmarzo/understanding-type-i-and-type-ii-errors/
If we get super crazy:
I'm curious as to whether or not my 2 main e-mail addresses show any difference in usage. for month in 2008, I saved all e-mail sent directly to me (ignorning spam). The two data sets are as follows:
Part One:
E-mail A: 7, 5, 21, 11, 0, 7, 19, 6, 5, 20, 2, 3, 12, 18, 12, 12, 17, 4, 5, 6, 12, 4, 1, 36, 2, 0, 6, 7
E-mail B: 10, 12, 12, 11, 1, 1, 4, 4, 6, 10, 6, 2, 7, 7, 8, 11, 9, 3, 5, 17, 9, 7, 4, 13, 7, 5, 4, 3
we're going to say that the standard deviation for the population of emails on a day is 5
for this question, don't worry about whether or not the data is skewed. It plays a minor role, but as we know, the means of a sample will tend towards the mean of a population regardless. Still, run the 1.5IQR test and see if there's anything severe that we should take out of either data set. If you think we should take something out, explain why.
Give a 95% CI for E-mail A.
Give a 95% CI for E-mail B.
Can we say that one of the E-mail addresses gets more e-mails than the other using the information we have here? Give one or two sentences explaining your position on the matter.
Why did we not use a null and alternate hypothesis for this question? In other words, why didn't we set the mean of e-mail A as the population mean, set a null hypothesis that e-mail A mean is the same as e-mail B's mean and run through with an alpha of 0.05?