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Lecture 4

# Lecture 4 - Jan 18.doc

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Department
Psychology
Course Code
PSYC 305
Professor
Heungsun Hwang

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PSYC305 Lecture 4 - Jan. 18 Limitations of z-test: • Knowing the true value of the standard deviation of a population is unrealistic Alternative? - t-test • • Where standard deviation of population is unknown Hypothesis Testing About a Single Mean: t-test: • Purpose: • To test whether a sample mean significantly differs from a population mean • Prior Requirements/Assumptions: • The population is normally distributed • The mean of the population must me known • The sample must be a simple random sample of the population Thus, t statistic is obtained by replacing the standard deviation of the population mean with the • sample counterpart in z statistic • Due to this replacement, t statistic does not follow the standard normal distribution anymore. In- stead, it follows the t-distribution • The t-distribution was discovered by William S. Gosset in 1908. Gosset was a statistician employed by the Guinness brewing company which had stipulated that he not publish under his own name. He therefore wrote under the pen name ‘Student’. • Also called Student’s t distribution The t Distribution: • Varies in shape according to the degrees of freedom (DF) = N-1 • The t distribution approaches the standard normal distribution as DF becomes large • The approximation is quite good for DF > 30 Hypothesis Testing About a Single Mean: t-test: • Calculate the value of t-statistic (or simply t-value) for your sample mean with µ and M M Look into how extreme your t-value is • • Look at the table of t values and find the critical
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