We continued with the z-based confidence intervals (CI) where σ is known. We completed the discussion of the CI calculation for the physicians' taxable incomes example. The important thing to remember is that a CI gives us the probability (e.g., 95%) of finding the true but the unknown mean μ in that interval.
When σ is not known, then we can't use the z-distribution, but fortunately, we have the t-distribution at our disposal (due to William Gosset, a.k.a. "Student"). This distribution is more variable than z, but when the sample size increases beyond 30, it too is approximated by the normal.
The important question of how to find the best sample size n was discussed in the context of the physicians' taxable incomes. We also looked at the problem when σ is not known. (Take a preliminary sample of size m, and continue!)
What about the CI for a proportion? This was motivated by looking at the election polling results. Towards the end of the class, we did an experiment using an inflatable globe and found the estimate of the proportion of water (oceans, lakes, etc.) to the total surface area of the globe. In each section the estimated proportion ended up being very close to the true 70.8% after taking only 30 samples. (The students randomly picked a point on the globe as either water (W) or land (L). I will post the video I took in Section C02 on YouTube a little later.
The midterm exam took place this week on November 5, 2010, at 5:00 pm in Great Hall, RJC.
1 comment:
Hi Professor,
The midterm was quite a challenge! Thanks for the 15-minute extension, it really helped!
Tien
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