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Distribution of Sample Means

Distribution of Sample Means. 2011, 10, 20. Today ’ s Topics. What is distribution of sample means?** Properties of distribution of sample means* How to find out the probability of a sample (mean)?**. ― Weekly Mean. Example 1: Jamie Joan ’ s.

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Distribution of Sample Means

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  1. Distribution of Sample Means 2011, 10, 20

  2. Today’s Topics • What is distribution of sample means?** • Properties of distribution of sample means* • How to find out the probability of a sample (mean)?**

  3. ― Weekly Mean Example 1: Jamie Joan’s • The sales of food and drink in Jamie Joan’s vary from day to day. The distribution of daily sales is a normal distribution with mean of  = $900 and a standard deviation of  = $300. • We plot all weekly mean sales • Where would the weekly means fluctuate around? • How much variability would you expect in the distribution of weekly means? Distribution of Weekly Means

  4. Distribution of Sample Means • If the sample size is large (n > 30) Population Distribution of sample means “Good”

  5. Properties of distribution of sample means – Central Limit Theorem • For any population with mean  and standard deviation , the distribution of sample means for sample size n will approach a normal distribution with a mean of  and a standard deviation of as n approaches infinity. (good approximation if n > 30). • Mean: • Standard Error:

  6. ― Weekly Means Example 1: Jamie Joan’s • The sales of food and drink in Jamie Joan’s vary from day to day. The distribution of daily sales has mean of  = $900 and a standard deviation of  = $300. • Questions • What is the probability that a weekly mean is between $560 and $1,240? • What is the probability that a weekly mean is at or greater than $900? • The mean sales for last week is $1,100. Did they have an exceptional week? (Hint: What is the probability of having a weekly mean of $1,100 or higher?) $560 $1,240

  7. p = ? Your Turn: IQ Score • Population IQ: • Distribution of Sample Means (n = 75)

  8. How to Find out the Probability of a Sample Mean – Four Steps • List the population parameters: • Compute and list the mean and standard error of the distribution of sample means • Compute the z score • From the Unit Normal Table, look for the probability of z

  9. Distribution of sample means X Population s Sample m s Notations

  10. Lecture Recap: Distribution of Sample Means • What is a distribution of sample means? • Central Limit Theorem (Properties of a distribution of sample means) • Shape • Mean • Standard error • How to use a distribution of sample means to find out the probability of a sample mean? • Notations for population distribution, sample distribution, and distribution of sample means

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