6.3 THE CENTRAL LIMIT THEOREM. DISTRIBUTION OF SAMPLE MEANS  A sampling distribution of sample means is a distribution using the means computed from.

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Presentation transcript:

6.3 THE CENTRAL LIMIT THEOREM

DISTRIBUTION OF SAMPLE MEANS  A sampling distribution of sample means is a distribution using the means computed from all possible random samples of a specific size taken from a population  Ex: A researcher selects a sample of 30 males and finds the mean of the age to be 30 for the first sample, 28 for the second, and 35 for the third, etc. The means will become a random variable that we can study.

SAMPLING ERROR  The difference between the sample measure and the corresponding population measure  *This is because the sample is not a perfect representation of the population

PROPERTIES OF THE DISTRIBUTION OF SAMPLE MEANS  1. The mean of the sample means will be the same as the population mean.  2. The SD of the sample means will be SMALLER than the SD of the population, and it will be equal to the population SD divided by the square root of the sample size.

THE CENTRAL LIMIT THEOREM

EXAMPLE  Children between the ages of 2 and 5 watch an average of 25 hours of TV per week. Assume the variable is normally distributed and the SD is 3 hours. If 20 children are randomly selected, find the probability that the mean number of hours they watch television will be greater than 26.3 hours.

EXAMPLE  Children between the ages of play an average of 20 hours of video games per week. Assume the variable is normally distributed and the SD is 4 hours. If 30 children are randomly selected, find the probability that the mean number of hours they watch television will be less than 18 hours.

 The average age of a vehicle registered in the US is 96 months. Assume the standard deviation is 16 months. If a random sample of 36 vehicles if selected, find the probability that the mean of their age is between 90 and 100 months.

WHAT’S THE DIFFERENCE?