9.3 power point

8/8/2019 9.3 Power Point

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Sampling DistributionsSampling Distributions

Section 9.3Section 9.3


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Do You Really Mean That?Do You Really Mean That?

We use proportions in statistics most oftenWe use proportions in statistics most oftenwhen we are interested in categoricalwhen we are interested in categorical

variables.variables.

When we record quantitative data, we areWhen we record quantitative data, we areinterested in the mean or median instead.interested in the mean or median instead.


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The Mean and Standard Deviation ofThe Mean and Standard Deviation of

a Sample Meana Sample Mean


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Try To Be On Your Best BehaviorTry To Be On Your Best Behavior

The behavior of in repeated samples is much likeThe behavior of in repeated samples is much likethat of the sample proportion :that of the sample proportion :

The sample mean is an unbiased estimator of theThe sample mean is an unbiased estimator of the

population meanpopulation mean ..

The values of are less spread out for larger samples.The values of are less spread out for larger samples.Their standard deviation decreases at the rate , so youTheir standard deviation decreases at the rate , so youmust take a sample four times as large to cut the standardmust take a sample four times as large to cut the standard

deviation of in half.deviation of in half.

You should only use the recipe for the standard You should only use the recipe for the standarddeviation of only when the population is at least 10 timesdeviation of only when the population is at least 10 timesas large as the sample.as large as the sample.

xp

x

x

x

x

n

n

W


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You Were Always On My MindYou Were Always On My Mind

Notice that these facts about the mean andNotice that these facts about the mean andstandard deviation of are truestandard deviation of are true no matterno matter

what the population distribution looks likewhat the population distribution looks like..

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But What About Shape?But What About Shape?


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A Tall TaleA Tall Tale

Remember that young womens heightsRemember that young womens heightsare ~are ~NN (64.5, 2.5). So what is the(64.5, 2.5). So what is the

probability that a randomly selected youngprobability that a randomly selected youngwoman is taller than 66.5 inches?woman is taller than 66.5 inches?

What is the probability that the meanWhat is the probability that the meanheight of an SRS of 10 young women isheight of an SRS of 10 young women isgreater than 66.5 inches?greater than 66.5 inches?


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Averages of several observations are lessAverages of several observations are less

variable than individual observations.variable than individual observations.


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Absolutely AbnormalAbsolutely Abnormal

Although many populations have roughlyAlthough many populations have roughlynormal distributions, very few are exactlynormal distributions, very few are exactlynormal. What happens to when thenormal. What happens to when the

population distribution is not normal?population distribution is not normal?

Well, what did you see it the computer activityWell, what did you see it the computer activityon Friday?on Friday?

This famous fact of probability is called theThis famous fact of probability is called theCentral Limit Theorem.Central Limit Theorem.

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The Central Limit TheoremThe Central Limit Theorem

* How large a sample size n is needed for to be close toNormal depends on the population distribution. Moreobservations are required if the shape of the populationdistribution is far from Normal.

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The histogram in Display 5.9 shows theThe histogram in Display 5.9 shows the

distribution of exam scores for 192 students in andistribution of exam scores for 192 students in anintroductory statistics course at the University ofintroductory statistics course at the University ofFlorida.Florida.


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Match the histograms A, B, and C in Display 5.10 to theirMatch the histograms A, B, and C in Display 5.10 to theirdescriptions, I, II, or III.descriptions, I, II, or III.

I. The individual scores for one random sample of 30I. The individual scores for one random sample of 30students.students.

II. A simulated sampling distribution of the mean ofII. A simulated sampling distribution of the mean ofthethe scores of 100 random samples of 4 students.scores of 100 random samples of 4 students.

III. A simulated sampling distribution of the mean ofIII. A simulated sampling distribution of the mean ofthethe scores of 100 random samples of 30 students.scores of 100 random samples of 30 students.


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Lets Get TechnicalLets Get Technical

The time it takes a technician to performThe time it takes a technician to performpreventative maintenance on an air conditioning unitpreventative maintenance on an air conditioning unitis governed by the exponential distribution whoseis governed by the exponential distribution whosedensity curve is shown below. The mean time is 1density curve is shown below. The mean time is 1hour and the standard deviation is one hour. Yourhour and the standard deviation is one hour. Yourcompany has a contract to maintain 70 of these unitscompany has a contract to maintain 70 of these unitsin an apartment building. You must schedulein an apartment building. You must scheduletechnicians time for a visit to this building. Is it safetechnicians time for a visit to this building. Is it safeto budget an average of 1.1 hours for each unit orto budget an average of 1.1 hours for each unit orshould you budget an average of 1.25 hours?should you budget an average of 1.25 hours?

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