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UMass Amherst PSYCH 240 - Confidence Intervals

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Psych 240 1st Edition Lecture 16Current LectureExplaining Everything-SM tells us how much sample means tend to vary from a population meanoA low SM means that every sample mean comes out relatively close to the true population meanoA high SM means that some of the sample means can actually come out relatively far from the population mean-We use t scores to measure whether or not a sample mean is unexpectedly far from a population meanoT scores far from zero indicate that the sample mean is farther from population mean than we would usually expect to see oWe get t by seeing how far a sample mean is from the population mean and dividing this by how much sample means tend to vary from the value (SM)-A critical value is a cutoff we set for how unexpected a sample mean has to be for us to say we have evidence against a given population meanoWe want to rule things out that seen too high and too low for our sample while making sure that there is only a 1% chance that we'll rule out the true answer Effects of Increased Sample Size-The standard error of the mean decreases when sample size increases-Each mean from a large sample tends to be close to the true population mean, so the sample means are very consistent from one sample to the nest-So the standard deviation of the distribution of means is lower for larger samplesClicker Questions-A random sample of 36 college graduates in 2014 had a mean student loan debt of $37,100 with a standard deviation of $7200. Compute the 95% confidence interval.oSM=7200/square root of 36oLCL = 37100 - (2.03 x 1200) = 34,664oUCL= 37100 + (2.03 x 1200) = 39,536 Objectives-Be able to compute the confidence interval for the mean given the mean, standard deviation, and sample size for a sample of scores. These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.-Understand confidence intervals and how they relate to hypothesis tests. Know what it means for a value to fall inside or outside of a confidence interval. -Understand how the width of a confidence interval is related to alpha and sample size. Understand what alpha means for a confidence interval. Be able to explain why 95% and 99% confidence intervals have different widths. -Know the probability that a confidence interval will include the true population mean, and be able to explain why this is the case. Understand that every new sample will have a different confidence interval, but the true population mean does not change from sample to sample. -Be able to decide whether a single-sample t test would be significant or non-significant given a confidence interval and the hypothesized population mean. -Be able to compute the confidence interval for the mean of difference scores given the mean, standard deviation, and sample size for a sample of difference scores. -Know the relationship between the confidence interval on the mean of difference scores and the result of a dependent-samples t test. Given a null hypothesis that specifies a particular difference between the population means of the two samples, be able to say whether a dependent-samples t-test for this null hypothesis would be significant or non-significant just by looking at the


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