Inferences Based on a Single Sample

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Inferences Based on a Single Sample

• Chapter 7

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Large-Sample Confidence Intervals for a
Population Mean

• I. Definitions
• A. Interval Estimator (or confidence interval) is
  a formula that tells us how to use sample data to
  calculate an interval that estimates a population
  parameter.
• B. Confidence Coefficient is the probability that
  the interval estimator encloses the
  parameter-that is the relative frequency with
  which the interval estimator encloses the
  parameter when the estimator is used repeatedly a
  large number of times.

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Large-Sample Confidence Interval for

• Note when
• is unknown, then for a large sample you may
  substitute s

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Confidence Coefficients and the Associated
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Homework

• Section 7.1, Pages 294-297,7.1,7.2,7.3,7.6,7.14,7
  .18

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7.2 Page 294

• B) What is the confidence level for the interval
• Answer 90

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7.3

• Find a 95 confidence interval
• Answer

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7.14 Page 295

• a) Give a point estimate for the population mean
• b) Construct a 98 confidence interval
• c) What assumption must hold? Ans the Central
  Limit Theorem says that for large n, sampling
  distribution is approx normal.

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Small Sample Confidence Interval for the
Population Mean Section 7.2

• When your sample size is small (n less than 30)
  and your population is NORMAL, you may make a
  small sample confidence interval for the true
  mean of the population by the following formula

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T-Distribution

• The T-Distribution is a family of bell-shaped
  curves. The specific curve needed for any
  particular situation depends on the degree of
  freedom. The degree of freedom is (n-1).

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Homework Section 7.2

• Pages 305-308, 7.21, 7.22, 7.23, 7.27, 7.34

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7.34

• Estimate the true mean adrenocorticotropin level
  of sleepers using a 95 confidence interval.

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Large-sample Confidence Interval for the
Population Proportion
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Large Sample Confidence Interval for p
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Homework Section 7.3

• Pages 313-314, 7.37, 7.38, 7.39, 7.40, 7.43,
  7.49

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7.38

• A random sample of
• A) Is sample large enough to construct a
  cofidence interval as has been discussed? (Yes)
• B) Construct 95 confidence interval

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Determining the Sample Size- Section 7.4

• In order to estimate the population mean with a
  bound, B, with
• The required sample size is found as follows

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Determining the Sample Size for a Binomial
Population

• In order to estimate a binomial probability
  within bound, B, the required sample size is
• If p is unknown, it can be estimated by letting
  p.5q
• This will give you a conservative value for the
  sample size.

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Homework section 7.4

• Pages 320-321
• 7.51,7.52,7.53,7.54,7.64