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Chapter 7

Chapter 7. Estimation Procedures. Basic Logic . In estimation procedures, statistics calculated from random samples are used to estimate the value of population parameters . Example:

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Chapter 7

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  1. Chapter 7 Estimation Procedures

  2. Basic Logic • In estimation procedures, statistics calculated from random samples are used to estimate the value of population parameters. • Example: • If we know 42% of a random sample drawn from a city are Conservatives, we can estimate the percentage of all city residents who are Conservatives.

  3. Basic Logic • Information from samples is used to estimate information about the population. • Statistics are used to estimate parameters. POPULATION SAMPLE PARAMETER STATISTIC

  4. Sampling Distribution is the link between sample and population. The value of the parameters are unknown but characteristics of the Sampling Distribution are defined by theorems. Basic Logic POPULATION SAMPLING DISTRIBUTION SAMPLE

  5. Two Estimation Procedures • A point estimate is a sample statistic used to estimate a population value. • A newspaper story reports that 74% of a sample of randomly selected British Conservative voters support David Cameron as the new Conservative party leader • Confidence intervals consist of a range of values. • ”between 71% and 77% of British Conservative voters approve of David Cameron as leader .”

  6. Constructing Confidence Intervals For Means • Set the alpha (probability that the interval will be wrong). • Setting alpha equal to 0.05, a 95% confidence level, means the researcher is willing to be wrong 5% of the time. • Find the Z score associated with alpha. • If alpha is equal to 0.05, we would place half (0.025) of this probability in the lower tail and half in the upper tail of the distribution. • Substitute values into formula 7.1.

  7. Confidence Intervals For Means • For a random sample of 178 households, average TV viewing was 6 hours/day with s = 3. Alpha = .05. • See formula 7.2 • c.i. = 6.0 ±1.96(3/√177) • c.i. = 6.0 ±1.96(3/13.30) • c.i. = 6.0 ±1.96(.23) • c.i. = 6.0 ± .44

  8. Confidence Intervals For Means • We can estimate that households in this community average 6.0±.44 hours of TV watching each day. • Another way to state the interval: • 5.56≤μ≤6.44 • We estimate that the population mean is greater than or equal to 5.56 and less than or equal to 6.44. • This interval has a .05 chance of being wrong. • So: With a probability of 95%, we can state that the households in this community watch on average between 5.56 and 6.44 hours of TV each day

  9. Confidence Intervals For Means • Even if the statistic is as much as ±1.96 standard deviations from the mean of the sampling distribution the confidence interval will still include the value of μ. • Only rarely (5 times out of 100) will the interval not include μ.

  10. Constructing Confidence Intervals For Proportions • Procedures: • Set alpha. • Find the associated Z score. • Substitute the sample information into Formula 7.3. See Healey’s book for more information

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