- Last Time: Sampling distribution of a
proportion
- proportions too can be turned into Z-values
- table values can be "off the charts": then what?
- Calc -> Probability Distributions -> Normal
- If you have a Z, Cumulative probability
- If you have a total area to the left and
want a Z, Inverse Cumulative probability
- Today:
- Collect homework for 9.1-9.2
- Homework for section 9.3 will be due Tuesday, 2/24.
- Homework for sections 10.1-3 will be due the following Tuesday,
3/2.
- Chapter 10: sections 10.1-10.3 - Confidence Intervals
- point estimators versus interval estimators
- unbiased estimator
- has the same mean as that of the parameter
- This is why there's an n-1 in the sample
variance formula.
- consistent estimator
- gets better with increasing sample size
- Between two unbiased estimators, the one with smaller
variance is relatively efficient:
- The sample mean and sample median both estimate
the mean mu, but the variance of the sample
mean is smaller. Hence the sample mean is
relatively efficient compared to the median.
- Basic idea of confidence
interval estimator of mu (p. 302)
- We're going to build a cage around a point
estimator, that we hope captures the parameter.
- Using a wider cage means you're more likely to
catch it, but by using a larger cage you're not
saying as much!
- You want to be right a goodly amount of the time
(e.g. 90%, 95%). Confidence is related to size
of the confidence interval, however.... There's
a price!
- Example: 10.54,
p. 313
- Examine the histogram to test their statement of normality
- Find confidence intervals for standard values of the
significance level alpha (p. 302)
- Chapter 10: sections 10.4 - Sample size
- If you want to squeeze down your interval, your box, to a
given size, then you need to figure out the sample size you need to do so.
- Example: 10.66
- Next time: More on chapter 10
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