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 managers 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 605 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 (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 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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