Psych110Ch9Presentation Revised - Chapter 9 Introduction to the t statistic The t Statistic allows researchers to use sample data to test hypotheses

# Psych110Ch9Presentation Revised - Chapter 9 Introduction to...

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Chapter 9: Introduction to the t statistic
The t Statistic allows researchers to use sample data to test hypotheses about an unknown population mean . does not require any knowledge of the population standard deviation (needed when using z-score) can be used to test hypotheses about a completely unknown population; that is, both μ and σ are unknown , and the only available information about the population comes from the sample.
The t Statistic required for a hypothesis test using t-stat a sample a reasonable hypothesis about the population mean.
The t StatisticTwo general situations where the t-statistic is used in hypothesis testing: 1. to determine whether or not a treatment causes a change in a population mean. must know the value of μfor the original, untreated populationObtain a sample from the population the treatment is administered to the sampleIf the resulting sample mean is significantly different from the original population mean, can conclude that the treatment has a significant effect
The t Statistic 2.a hypothesized valuefor an unknown population mean is derived from a theory or other predictionObtain a sample from the populationthe t statistic is used to compare the actual sample mean with the hypothesized population meansignificant difference indicates that the hypothesized value for μshould be rejected
The Estimated Standard Error and the t Statistic sampling error (discrepancy or "error" between the sample mean and the population mean) is expected Is the discrepancy observed between sample mean and population mean significant? Find out through hypothesis testings
The Estimated Standard Error and the t Statistic Two alternatives to consider in hypothesis testing: 1. Discrepancy between M and μ is simply due to sampling error and not resulting from treatment effect OR 2.Discrepancy between M and μ more than what is expected by sampling error alone , therefore the sample mean significantly different from the population mean
The Estimated Standard Error and the t Statistic The critical first step for the t statistic