Central Limit Theorem Sample Proportions.

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Presentation transcript:

Central Limit Theorem Sample Proportions

Requirements Random sample from population?

Conclusions Shape of sampling distribution is approximately normal Mean of the sampling distribution is equal to the population proportion Standard deviation of the sampling distribution is equal to the following formula

“Watch Out” on page 266

Why is the CLT important?? See problem 13-3 on page 267

Examples of CLT for Proportions “AP Guidelines”

You take an SRS of 100 households and find that 17 households have a pet cat. Where does your sample proportion fall in this sampling distribution? Is your sample result surprising? Do you think that 25% of Solon households have a pet cat? Suppose that 25% of all households in Solon have a pet cat. What would be the shape, mean, and standard deviation of sample proportions of sample size 100? Why? Check Requirements Random sample from pop? Stated SRS (YES) (YES) Requirements met Shape is approximately normal Since the probability of getting a sample proportion of 17% or less, if 25% of Solon households have cats, is only 3.2%, I suspect that less than 25% really have cats.

Example A study was conducted in 2000 which surveyed a random sample of men between the ages of 45 and 54. The researchers reported that 71.3% of such men are considered overweight. If a random sample of 90 men in this age group is selected, what is the probability that more than 70% of them will be overweight?

A study was conducted in 2000 which surveyed a random sample of men between the ages of 45 and 54. The researchers reported that 71.3% of such men are considered overweight. If a random sample of 90 men in this age group is selected, what is the probability that more than 70% of them will be overweight? Check requirements Random sample from pop? Stated Random YES YES Conclusions Shape of samp. dist. is approx. normal