Psyc_315_-_Winter_2010_-_Class_16

# Psyc_315_-_Winter_2010_-_Class_16 - Z-Test and Confidence...

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Unformatted text preview: Z-Test and Confidence Intervals (Estimation) 2 Hypothesis Testing vs Estimation • For some problems, hypothesis testing is inappropriate and estimation is the only relevant approach. • Example: The manager from the university bookstore wants to know how much money the student body, on average, has available for textbook purchases this term. She polls a random sample of all students. • Try to think of a meaningful H o that the bookstore manager might specify. • H o : Population M = \$50? H o : Population M = \$250? • No specific H o immediately presents itself. • The bookstore manager’s interest is more exploratory: She wishes to estimate population M from the sample results, not test a specific value of population M as indicated by H o . 3 Point Estimation vs Interval Estimation • A point estimate is a single value, a point, taken from a sample and used to estimate the corresponding parameter of a population. – Use M, SD M , SD 2 M to estimate Population M, SD, SD 2 respectively. – Example: 55% of voters prefer candidate Joe. You have been given a point estimate of voter preference in the population. 4 Point Estimation vs Interval Estimation • An interval estimate is a range of values, an interval, within which it can be stated with reasonable confidence the population parameter lies. – E.g., We might state that the average heart rate is 60±5 beats per minute with 95% confidence. – In this case the 95% confidence interval is 55 to 65. – What does it mean to say we have 95% confidence in an interval estimate? 5 Construct Interval Estimate of Population Mean • 95% of all sample means fall within ±1.96 SD M of Μ (two- tailed) • Consequently, for 95% of all sample means population M is no more than 1.96(SD M ) away. • So the interval will contain population M 95% of the time. • This is the 95% confidence interval. 1.96( ) M M SD ± 6 Interval Width and Level of Confidence • Rule for the 95% confidence interval (SD M known) • Rule for the 99% confidence interval (SD M known) • General rule for a confidence interval (SD M known) 1.96( ) M M SD ± 2.58( ) M M SD ± ( ) M M Z SD α ± 7 Interval Width and Sample Size • The width of a confidence interval depends on the number of scores (n) in the sample....
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Psyc_315_-_Winter_2010_-_Class_16 - Z-Test and Confidence...

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