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lecture13

# lecture13 - Large sample 100(1 C.I for The large-sample...

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Large sample 100(1 - α )% C.I. for μ I The large-sample 100(1 - α )% confidence interval for μ is ¯ x ± z α/ 2 σ ¯ x = ¯ x ± z α/ 2 σ n where z α/ 2 is the z value with an area α/ 2 to its right and σ ¯ x = σ/ n . The parameter σ is the standard deviation of the sampled population and n is the sample size. Remark: When σ is unknown and n is large (say, n 30), the confidence interval is approximately equal to ¯ x ± z α/ 2 s n where s is the sample standard deviation.

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Exercise 12.2 from last lecture I A random sample of 90 observations produced a mean ¯ x = 25 . 9 and a standard deviation s = 2 . 7. a. Find a 90% confidence interval for μ b. Find a 99% confidence interval for μ
Small-sample confidence interval I There are many actual needs to address small samples. For example, Federal legislation requires pharmaceutical companies to perform extensive tests on new drugs before they can be marketed. After testing on animals, and if it seems safe, then the company can try it out on humans.

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lecture13 - Large sample 100(1 C.I for The large-sample...

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