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Statistics of Psychology and Sociology
(PSYC/SOCI 2317)**

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Exam #2: Learning Objectives and Review
Questions**

Students are strongly encouraged to take advantage of the “learning check” exercises in each chapter, the “demonstrations” at the end of each chapter, and the odd numbered homework problems (the answers to the odd numbered problems are in the back of the book). See also the “study hints” in the preface of your textbook. The following learning objectives, questions, and information is designed to focus your preparatory efforts and do not necessarily constitute specific questions that will appear on the exam. The only formulas that will be provided for the exam are those that are listed on the inside covers of your textbook. The necessary tables listed in the Appendix will also be provided.

Learning objectives – students should be able to demonstrate the following:

- Identify the appropriate use of z-scores.
- Determine what the z-score measures.
- Differentiate standardized distributions from other distributions.
- Calculate the z-score when given a raw score (X), mean, and standard deviation.
- Locate the relative position of a z-score in a distribution.
- Use z-scores to compare one raw score against another.
- Calculate the raw score (X) when given a z-score, mean, and standard deviation.
- Address the following questions.

What does the sign (+ or -) of the z-score indicate? What does the number indicate? After sketching a normal distribution, could you identify the approximate locations of the following z-scores: 0.25, 1.20, 0.00, -0.80, and -2.25? Which of these are centrally located? Which of these are extreme? When a normal distribution is transformed to a distribution of z-scores, what is the value of the mean and standard deviation of this transformed distribution? What information do you need to know in order to transform a raw score to a z-score (hint: consult the z-score formula)? How do you determine the values of raw scores from z-scores? For scenarios like, “If Joe’s math test score was 75, and Mary’s history test score was 45, who would expect to get the better grade,” what information would you need to know in order make this comparison? How would you go about solving this type of problem? [hint: convert each raw score to a z-score first, then compare the z-scores]

Learning objectives – students should be able to demonstrate the following:

- Differentiate proportion from percentage.
- Define the term probability.
- Determine the requirements for random sampling.
- Describe the properties of the normal distribution.
- Identify the information that is listed in the unit normal table (Table B-1), and know how to use this table.
- Determine probabilities when given expressions like: p(X > 130), p(X < 50), and p(75 < X < 125), when the mean and standard deviation are given.
- Address the following questions.

What is wrong with the following expressions: (p = 1.25) and (p = -0.56)? What is the unit normal table (Table B-1 in the Appendix) and what purpose does it serve? What information is listed in the unit normal table? How do you determine the proportion between a negative and a positive z-score? How would you determine the value of a raw score when given statements like, “What raw score separates the top 20% from the rest?” [hint: use a known proportion to determine the z-score using Table B-1, then transform the z-score to a raw score.]

Learning objectives – students should be able to demonstrate the following:

- Define the term sampling error.
- Differentiate the distribution of sample means from other distributions.
- Define the central limit theorem.
- Determine the expected value of the sample mean.
- Calculate the standard error of the mean and understand what it measures.
- Determine the relationship between sample size (n) and the standard error of the mean.
- Convert sample means to z-scores and locate them in the distribution of sample means.
- Determine the probability of obtaining a specific sample mean when given: a population mean, a population standard deviation, and a sample size (n).
- Determine the consequences of selecting larger or smaller sample sizes with respect to the value of the standard error of the mean, the resulting z-score, and probabilities.
- Address the following questions.

What do we call the standard deviation of the distribution of sample means? How is it calculated? What does it measure? What is the central limit theorem? What is the expected value of the mean equal to? If a population has a standard deviation of 10 points: (a) if a single score is selected from this population, how close to the population mean, on average, would you expect the score to be; and (b) if a sample of n = 16 scores is selected from the population, how close to the population mean, on average, would you expect the sample mean to be (hint: see page 160)? What steps would you follow to convert a sample mean to a z-score? Once you have converted a sample mean to a z-score, how do you determine the probability of obtaining a sample mean that is greater than (or less than) this value? [hint: use Table B-1]

Learning objectives – students should be able to demonstrate the following:

- Determine the purpose of hypothesis testing and the logic of its use.
- Differentiate each of the four steps of hypothesis testing and their order.
- Differentiate the null hypothesis from the alternative hypothesis.
- Define the concept: alpha level.
- Differentiate Type I from Type II error.
- Compute a z-score, and make the appropriate decision and conclusion on the basis of the computed z-score.
- Differentiate two-tailed from one-tailed hypothesis tests.
- Address the following questions.

What symbols are used to express these null and alternative hypotheses? Why must we set a criterion for making a statistical decision? What is the alpha level? What is another name for alpha level? What is the “critical region” in a sampling distribution? Where is it located in a sampling distribution? Why is it necessary to compute a test statistics (like the z-score) in order to make a statistical decision? What statistical decisions are possible? What does it mean when we reject the null hypothesis? What does it mean when we retain it (or “fail to reject it”)? What would our statistical decision be if our test statistic were located in the critical region (shaded portion) of the sampling distribution? How is the z-score used as a test statistic? How can we control the probability of committing a Type I error? What is a “non-directional” hypothesis test? When would a one-tailed hypothesis test be used?

Learning objectives – students should be able to demonstrate the following:

- Identify the circumstances in which a t-test should be used to test the null hypothesis instead of a z-score.
- Differentiate the t-test formula from the z-score formula.
- Identify how the t-distribution differs from the normal distribution.
- Understand how to use Table B-2 in the Appendix.
- Determine how critical values of the t-test are determined and the information that one must have in order to determine the critical values.
- Compute the
*estimated*standard error of the mean. - Compute a t-test and make the appropriate statistical decision on the basis of the computed t-test.
- Address the following questions.

Under what circumstances
would a t-test be used instead of a z-score for a hypothesis test? How does the
single sample t statistic formula differ from the z score formula? How does the
t distribution differ from the normal (z score) distribution? How do you
compute the *estimated* standard error of the mean? What does it measure?
How does it differ from the standard error of the mean (from Chapter 8)? Review
the concepts regarding the computation of the sum of squares (SS) and the sample
standard deviation from Chapter 4.