Chapter 8 Confidence Intervals

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Chapter 8Confidence Intervals

• 8.3
• Confidence Intervals about a Population Proportion

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Objectives

• Obtain a point estimate for the population
  proportion
• Obtain and interpret a confidence interval for
  the population proportion
• Determine the sample size for estimating a
  population proportion.

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• EXAMPLE Computing a Point Estimate
• In a Fox News Poll, 911 registered voters
  nationwide were asked Have you ever cheated on a
  person you were in a relationship with?
• Of the 911 respondents, 191 said yes.
• Obtain a point estimate for the proportion of
  registered voters that have cheated on a person
  they were in a relationship with.

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• EXAMPLE Computing a Point Estimate
• To obtain a point estimate for the proportion of
  registered voters that have cheated
• x / n
• 191 /911
• .2097 21

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• EXAMPLE Constructing a Confidence Interval
  for a Population Proportion
• In a Fox News Poll, 911 registered voters
  nationwide were asked Have you ever cheated on a
  person you were in a relationship with?
• Of the 911 respondents, 191 said yes.
• Compute a 95 confidence interval for the
  proportion of registered voters that have cheated
  on a person they were in a relationship with.

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• EXAMPLE Constructing a Confidence Interval
  for a Population Proportion
• Before we can compute the 95 confidence interval
  for the proportion of registered voters that have
  cheated, we need to check if
• np(1-p) 10
• .2097 a .05 n 911
• 911.2097(1-.2097) 10
• 151 10 TRUE
• So we can go ahead and construct the 95
  confidence interval

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EXAMPLE Constructing a Confidence Interval
for a Population Proportion To find the 95
confidence interval for the proportion of
registered voters that have cheated .2097 a
.05 n 911 a/2 .025 z .025 1.96
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EXAMPLE Constructing a Confidence Interval
for a Population Proportion .2097 n 911 z
.025 -1.96 .2097- 1.96
v.2097(1-.2097)/911 .20971.96
v.2097(1-.2097)/911 The 95 confidence interval
is ( 0.18323, 0.23609) Lets do it on the
calculator- See page 376.
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Sample Size Needed for a Specified Margin of
Error and Level of Confidence
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• EXAMPLE Determining Sample Size
• A sociologist wanted to determine the percentage
  of residents of America that only speak English
  at home. What size sample should be obtained if
  she wishes the estimate to be within 3 percentage
  points with 90 confidence assuming
• she uses the 2000 estimate obtained from the
  Census 2000 Supplementary Survey of 82.4.
• (b) she does not use any prior estimates.

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• EXAMPLE Determining Sample Size
• Using the prior estimate
• .824 a .10 E .03
  z.051.645
• .824(1-.824) (1.645/.03)2
• n 436.043
• So we round up to a sample size of 437.

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EXAMPLE Determining Sample Size (b) If she
does not use any prior estimates. a .10 E
.03 z.051.645 .25 (1.645/.03)2
n 751.67 So we round up to a sample size of
752.
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