PSYCH 210 1st EditionExam # 2 Study Guide Lectures: 9-17Chapter 7 (Distribution of Sample Means)- What is sampling error?o The natural discrepancy, or amount of error, between a sample statistic and its corresponding population parametero Statistics calculated from a sample will never be identical to parameters from the population; sampling error inevitable- What is the difference between a sample distribution and a sampling distribution (e.g., the sampling distribution of sample means)?o A sample distribution is a distribution of statistics obtained by drawing from a single sample of a populationo A Sampling Distribution is a distribution of statistics obtained by selecting all of the possible random samples of a specific size from a population- What is the Central Limit Theorem, and how does it apply to sampling distributions?o For any population with a mean μ and a standard deviation σ, the sampling distribution of sample means from sample size n will approach a normal distribution with a mean of μ and a standard deviation of σ/√n as n approaches infinityo The mean of a sampling distribution of sample means is an unbiased estimator of population μ- What is standard error, and how is it similar to and different from standard deviation?o Standard Error (σM) is the special standard deviation (σ) for sampling distributions and is equal to σ/√n(whereas standard deviation = σ)o The standard error provides a measure of how much distance is expected on average between a sample mean (M) and population mean (μ)- What factors affect the size of standard error?o Sample size: the larger the sample, the more accurately the sample represents its population (smaller σM) …”Law of Large numbers” at work- How are z-scores used to answer probability questions about sample means? Understand how to use the z-score formula to answer these probability questions.o The z-score tells exactly where the sample mean is located in relation to all the other possible sample means that could have been obtainedThe sign tells whether the location is above or below the mean and the number tells the distance between the location and the mean in terms of the number of standard deviationso Because we can find the probabilities (proportions) associated with z-scores in the table, we can use them to asses how likely a given sample mean is likely to have occurred, merely by chanceChapter 8 (Hypothesis Testing)- How are null and alternative hypotheses used to answer questions about treatment effects? Understand how to state null and alternative hypotheses, using statistical symbols and ‘plain English’.o H0 = Null Hypothesis: Predicts that Tx has NO effecto H1 = Alternative Hypothesis: Predicts that Tx DOES have an effecto You can NEVER prove a hypothesis correct (only prove them wrong)If Null Hypothesis is wrong, the alternative is assumed by defaulto Always state hypotheses in terms of population parameters - What are critical values/critical regions? How do they relate to the distribution of sample means under H0?o The critical region is composed of the extreme sample values that are very unlikely (as defined by the alpha level) to be obtained if the null hypothesis is true.o The boundaries for the critical region(s) are determined by the alpha level.o If sample data fall in the critical region, the null hypothesis is rejected.- How are alpha levels used to set critical regions? Why is an alpha level the same thing as the ‘level of significance’?o The extremely unlikely values, as defined by the alpha level, make up what is called the critical regiono To find the boundaries that separate the high-probability samples from the low-probability samples, we must decide exactly what is meant by “low” and “high” probability. This is accomplished by selecting a specific probability value, which is known as the level of significance, or the alpha levelo Alpha level = probability test will lead to Type I error- How do you decide whether or not to reject a null hypothesis?o If an observed z score falls outside the critical region, the null hypothesis is rejected- How are z-scores used in hypothesis testing? Understand how to do a z-test, and what values are necessary before you can use z.o z-score compare exactly where the sample mean is located relative to the hypothesized population mean from H0o We must know μ, σ and M to calculate a z-score!- What is Type I error? Type II error? Understand the decision matrix that delineates the two different types of error.o Type I error is False positive; saying the treatment had an effect when it actually didn’to Type II error is false negative; missing a real treatment effect- What factors should you take into consideration when selecting an alpha level?o What kind of error are you trying to reduce? The only way to reduce Type I error is by decreasing the alpha level o Power: ability to accurately identify a treatment that worksDecreasing alpha decreases powero Type II errorDecreasing alpha increases Type II error- What are the assumptions for hypothesis tests using z-scores (i.e., the z-test)?o Independent Sampleso Normal Distributiono Random Samplingo Standard Error- What is the difference between a directional and nondirectional hypothesis test? How are critical regions affected by your choice of a one- vs. two-tailed test?o In a directional hypothesis test, the statistical hypotheses (H and H) specify either an increase or a decrease in the population mean. That is, they make a statement about the direction of the effecto While the area of alpha is the same whether it is a directional or nondirectional test, where that area is distributed changes.The one critical region for an alpha on a directional test is larger than the two critical regions for a nondirectional test- What is statistical power? What factors affect power? Understand how these factors work by looking at powergraphically (i.e., using graphs of sampling distributions).o Power: ability to accurately identify a treatment that worksDecreasing alpha level decreases PowerIncreasing effect size increases powerSwitching from directional to nondirectional test decreases powerIncreasing sample size increases power- Know how to calculate power for a z-test.o Determine α and asses whether it is a directional or nondirectional testo Calculate z cut-off scoreo Convert z into H1 distribution raw scoreo Calculate new z-score for H1 distributiono Find