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Lesson 8 Lecture notes

# Lesson 8 Lecture notes - Lesson 8 Means and Proportions...

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Lesson 8: Means and Proportions Population Parameters and Sample Statistics S1 - A survey is carried out at a university to estimate the proportion of undergraduates living at home during the current term. Population: undergraduates at the university Parameter: the true proportion of undergraduates that live at home Sample: the undergraduates surveyed Statistic: the proportion of the sampled students who live at home used to estimate the true proportion S2 - A study is conducted to find the average hours college students spend partying on the weekend. Population: all college students Parameter: the true mean number of hours college students spend partying on the weekend Sample: the students sampled for the study Statistic: the mean hours of weekend partying calculated from the sample S1 is concerned about estimating a proportion p where p represents the true (typically unknown) parameter and [pronounced "p-hat"] represents the statistic calculated from the sample S2 is concerned about estimating a mean u where u [pronounced "mew"] represents the true (typically unknown) parameter and [pronounce "x-bar"] represents the statistic calculated from the sample. In either case the statistic is used to estimate the parameter. The statistic can vary from sample to sample, but the parameter is understood to be fixed. The statistic, then, can take on various values depending on the result of repeated random sampling. The distribution of these possible values is known as the sampling distribution. Overview of symbols The following table of symbols provides some of the common notation that we will see through the remaing sections.

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The difference between "paired" samples and "independent" samples can be most easily explained by the situation where the observations are taken on the same individual (e.g. measure a person's stress level before and after an exam) where independent would consist of taking observations from two distinct groups (e.g.
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