Name: Person #: Recitation: ___________ PSY207 Problem Set 3, Chapters 9 - 11 Using the space provided, report and clearly identify your answers to each question. Please show ALL your calculations and feel free to do so with additional sheets of paper. Please round your answers to two decimal places. 1.) A schoolteacher is concerned that her students watch more TV than the average American child. She reads that according to the American Academy of Pediatrics, the average American child in the population watches = 4 hours of TV per day. She records the number of hours of TV each of her six students watches per day. The times (in hours) is presented below. a) State your null and alternative hypotheses in terms of the research scenario. b.) What are your degrees of freedom and critical value(s) given an = .01 level? c.) What is the estimated standard error for this sample of school children? d.) Calculate your test statistic. e.) Given the alpha level of = .01, is the teacher's sample statistically different from the population? Write a conclusionary statement and be sure to report your results as it would appear in an APA compliant manuscript (e.g. t(df) = tobs, p < XX, see slides for details). 1 f.) What is the estimated effect size in this study in terms of Cohen's d? Do you characterize it as being small, medium or large? g.) Calculate 99% confidence interval. 2.) What is the sample variance and the estimated standard error for a sample of n = 9 scores with SS = 72? s2 = sM = 3.) Calculate the pooled variance for the following two samples: 2 = Sample 1: n1 = 11 and s2 = 12.5 Sample 2: n2 = 13 and s2 = 8.75 4.) A classic experiment by Dutton & Aron (1974) examined men's attraction to a female they met in either one of two conditions: on a high unstable, shaky bridge or on a low sturdy bridge. Later, they rated the attractiveness of the woman. The following data is a generated replica of this study. Attractiveness was rated as 1-10 with 10 being very attractive. The researchers want to evaluate how the independent variable (bridge height) affects attractiveness ratings. More specifically, they predict that those men in the higher bridge condition will rate the woman as being more attractive. a.) State your null and alternative hypotheses. b.) What are your degrees of freedom and critical value(s) given an = .05 level? 2 c.) What is the estimated standard error? d.) Calculate your test statistic. e.) Given the alpha level of = .05, what would the researchers conclude about bridge height and attractiveness ratings? Write a conclusionary statement and be sure to report your results as it would appear in an APA compliant manuscript (e.g. t(df) = tobs, p < XX, see slides for details). f.) What is the estimated effect size in terms of proportion of variance accounted for (r2)? Do you characterize it as being small, medium or large? g.) Calculate a 95% confidence interval. 5.) You've decided to use an intervention program for reading skills for at risk children (n = 25). At the start of the year, the kids take a standardized reading test for their age group. After a year of intervention, they take a follow-up standardized test. On average there was a 3 point difference between time one and time two scores across the students. The variance for these differences is 36. Your primary objective is to determine whether your intervention improved reading test scores. a.) State your null and alternative hypotheses: b.) What type of research design is this? Circle one: Matched or Repeated Measures c.) What are your degrees of freedom and critical value(s) given the = .05 level? 3 d.) Calculate your test statistic. e.) What would you conclude about the efficacy of the intervention? Write a conclusionary statement and be sure to report your results as it would appear in an APA compliant manuscript (e.g. t(df) = tobs, p < XX, see slides for details). f.) What is the effect size in terms of proportion of variance accounted for (r2)? Do you characterize it as being small, medium, or large? g.) Calculate a 95% confidence interval. Points below do not require responses. These are simply conceptual items that you should review for the exam. When comparing standard errors across dependent-sample and independent-sample, in general, which type of should have a smaller standard error? Why? o How does this difference relate to rejecting a truly false null hypothesis? Be able to differentiate between matched and repeated-measures designs What does a confidence interval represent? 4