Statistical Sciences 1024A/B Chapter 20: Chapter 20 - Inference About a Population Mean

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Statistical Sciences
Course Code
Statistical Sciences 1024A/B
Lori Murray

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March 21, 2017 Chapter 20: Inference About a Population Mean 20.1 Conditions for Interference About a Mean Assume the units that are measured are from a simple random sample. This is important! The SRS assumption is more important than the assumption that the measurements follow a Normal distribution In practice, the Normal distribution assumption can be relaxed somewhat Unless n is really small, it is enough that the distribution by symmetric, and single peaked What if the population standard deviation is unknown? o Replace the population standard deviation, with the sample standar deviation s o The population standard deviation is a parameter o The sample standard deivatin s is a statistic o s is an estimate of the population standard deviation The standard error o The standard deivatin of the sample mean is o The sample standard deviation (the estimated standard deviation) is o This estimate us also called standard error of the sample mean 20.2 The t Distribution The onesample t statistic and the t distributions o Draw a simple random sample of n observations from a normal distribution o The onesample t statistic is o The t statistic has a t distribution with n1 degrees of freedom o We use the notation t(n1)r short Degrees of freedom o The sample variance is o In view of the restriction there are n1 unknown quantities in difference or n1 degrees of freedom Comparing t and standard normal o Similarities Differences Symmetric about 0 Bigger spread Single peaked More probability in tail areas Bellshaped Less probability in the centre Increasing the degrees of freedom o As the degrees of freedom increase from the t distribution the density curves look more and more like a N(0,1) o Compare the t 16 degrees of freedom and the N(0,1)
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