Sampling distribution of proportions

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Sampling distribution of proportions
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Symbols

• N the sample size
• X the number of observations that fit the given
  characteristic

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Sample proportion

• Round value to 3 decimal places

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Example

• A survey of 2500 households showed that 1000 had
  more than 2 cars.

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A second survey results

• A survey of 2500 households showed that 800 had
  more than 2 cars.

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A third survey had results

• A survey of 2500 households showed that 1200 had
  more than 2 cars.

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• As different surveys are conducted, the sample
  proportion will change.
• These sample proportions will form a sampling
  distribution that is approximately normal.

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Mean and standard deviation
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Requirements

• Sample size is less than or equal to 5 of the
  population
• Value of np(1 - p) is at least 10

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Calculation of z score
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Example

• A nationwide study in 2003 indicated that about
  60 of college students with cell phones send and
  receive text messages with their cell phones. A
  random sample of 1136 college students with cell
  phones is obtained. What is the probability that
  665 or fewer college students send and receive
  text messages with their cell phone?

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Identify values
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Find z and probability
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Another example

• According to the National Association of
  Realtors, 23 of the roughly 8 million homes
  purchased in 2004 were considered investment
  properties. A random sample of 500 homes is
  obtained. What is the probability that at least
  25 were purchased as investment properties?

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Identify values
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Find z and probability
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Your Turn

• About 11 of Americans believe that Joan of Arc
  was Noahs wife (silly folks that they are). If
  a group of 55 college freshmen were asked if Joan
  of Arc was Noahs wife, find the probability that
  at most 9 would believe that she was.