Exam 2 Review Questions

Exam 2 Review Questions Note: The solution sheet is meant to help you identify where you might be going wrong, thus for the parts requiring calculations only the final answers are provided, not the work (since you have time to be able to work backward and figure out where you’re going wrong). Remember to show all the work when taking the exam. Chapter 7 Probability & Samples 1. Suppose that you draw 100 samples of size 30 and calculate the mean and standard error. If you then draw 100 samples of size 50 from the same population, you expect the mean ____________ and the standard error ____________. a. Be approximately the same; be larger. b. Be approximately the same; be smaller. c. Be smaller; be smaller. d. Be smaller; be larger. e. Be smaller; be approximately the same. 2. Imagine that samples are repeatedly taken from each population. If each sample has n=50 observations in it, for which population will the sampling distribution of the sample means be approximately normal? a. Population A b. Population B c. Population C d. All of the above 3. Which of the following conditions is enough to ensure that the sampling distribution of the sample means has a normal distribution? a. Samples of size n > 10 are drawn. b. The population of all possible scores is very large. c. At least 30 samples are drawn, with replacement, from the distribution of possible scores. d. Individual scores, x, are normally distributed. 4. If everything is held constant, which of the following is most likely to result in a larger standard error? a. A larger population mean. b. A smaller population mean. c. A larger sample size. d. A smaller sample size.

Chapter 8 Hypothesis testing 1. What are the steps of a hypothesis test? What additional information should you include when conducting a hypothesis test and why? 2. What is an alpha level ? If the alpha level is .01 what percentage of scores fall in the critical region? 3. Define the critical region for a hypothesis test and explain how we use it to support or reject our null and research hypotheses.

6. A researcher investigates whether cold medication affects mental alertness. It is known that scores on a standardized test containing a variety of problem-solving tasks are normally distributed with  = 64 and  = 8. A random sample of n = 16 teenagers and a sample of n = 25 adults are given the drug and then tested. On average, the teenagers scored an average of M = 58 and the adults scored an average of M = 65.5. a. Are the data sufficient to conclude that the medication significantly reduces mental alertness in teenagers? Test with  = .01. b. Are the data sufficient to conclude that the medication significantly increases mental alertness in adults? Test with  = .01.

Chapter 9 T-statistic 7. A study examines self-esteem and depression in children. A sample of 25 children with low self- esteem is given a standardized test for depression. The average score for the group is M = 93.3 and s = 2.5 . The national average score on this test for depression is  = 90. Do children with low self- esteem show significantly more depression at  = .05? 8. When do you use a z-test versus a t-test? 9. How does the shape of a t distribution compare with the normal distribution? How does the shape of a t distribution depend on sample size (n)? You may describe in words or by drawing.

Chapter 10 t-Test for independent samples 11. Describe the data that are collected for an independent-measures t-test and the hypotheses that the test evaluates. 12. Explain in your own words what pooled variance is. If you have two samples of different sizes (i.e. the n for each group is different), explain whether the value of the pooled variance is closer to the larger sample or smaller sample.

13. An educational psychologist studies the effect of frequent testing on retention of course material. In one of the professor's sections, students are given quizzes each week. The second section receives only two tests during the semester. At the end of the semester, both sections receive the same final exam, and the scores are summarized below. a. Do the data indicate that testing frequency significantly increases performance at the .01 level of significance? Frequent Quizzes Two Exams n = 15 n = 15 M = 82 M = 78 s 2 = 7.07 s 2 = 13.57 b. What percent of the increase in performance was due to the increase in testing frequency?

15. An independent measures study has n = 12 participants in each of the two samples. If t = 2.07, what would you conclude at the following levels of alpha, assuming a two-tailed test? a. α = .05 ______________ b. α = .01 ____ ______ ____ Chapter 11 t-Test for two related samples 16. Describe the data that are collected for a repeated-measures t-test and the hypotheses that the test evaluates. 17. How many degrees of freedom are in a repeated-measures study with n = 20 participants?

18. After a sample of n = 25 high school students took a special training course, their SAT scores averaged  M D = 18 points higher with SS = 9600. Based on this sample, can you conclude that the training course significantly changes SAT scores at the .05 level of significance?

20. Explain what Cohen’s d and r 2 measure when calculated for a t-test. 21. When would it be appropriate to use a repeated-measures design for a research study?

Formulas M = Σ x n s 2 = Σ ( x − M ) 2 n − 1 = SS n − 1 s = √ s 2 z = M − μ σ SE = ¿ σ M = σ x = σ √ n z i = M − μ σ M Cohen’s d for z-scores: d = M − μ σ r 2 = t 2 t 2 + df One-sample t-tests df = n − 1 t = M − μ s M s M = s √ n = √ s 2 n s 2 = SS df = Σ ( x − M ) 2 n − 1 s = √ s 2 = √ SS df = √ Σ ( x − M ) 2 n − 1 d = M − μ s CI →μ = M ±t α s M Independent Measures t-tests (a.k.a independent samples) d f total =( n ¿¿ A − 1 )+( n ¿¿ B − 1 ) ¿¿ s p 2 = SS A + S S B d f A + d f B = s A 2 ( d f A ) + ¿¿ s ( M A − M B ) = √ s p 2 n A + s p 2 n B t = ( M ¿¿ A − M B )−( μ A − μ B ) s ( M A − M B ) ¿ d = M A − M B s p CI →μ 1 − μ 2 = M A - M B ±t ∝ s ( M A − M B ) Repeated Measures t-tests (a.k.a. within person measures) df = n − 1 s D 2 = SS df = Σ ( x D − M D ) 2 n − 1 s D = √ s D 2 = √ SS df = Σ ( x D − M D ) 2 n − 1 s M D = s D √ n = √ s D 2 n t = M D − μ D s M D d = M D s D CI →μ D = M D ±t α s MD