| 11.5 | Confidence Intervals for the Population Mean |
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- Key Idea 1: Sample means will have a standard normal distribution...
Discussion -
In Chapter 8 we learned to standardize a normally distributed statistic...
Since according to the central limit theorem, when sampling from any population, X will be approximately normally distributed with mean m and standard deviation
provided n ³ 20, we know that
will be approximately normally distributed with a mean of 0 and a variance of 1 - that is, it will have a standard normal distribution.
- Key Idea 2: Now we will use this knowledge to find a 95% confidence interval for a population mean...
| Discussion |
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| Example and Simulated Experiment |
| Discussion |
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Because this estimate of the population standard deviation adds a further approximation to the normal approximation of the distribution of X , the rule of thumb used by most statisticians requires n ³30 (rather than 20) in order to use the central limit theorem to obtain a confidence interval for m when the estimator S is substituted for s. |