Extra Practice problem set : Single Sample ttest Use an alpha of .05 1. A researcher was interested in whether an educational video on the importance of exercise had an effect on the number of times per week that college students exercised. To examine this issue, a research study was conducted in which a group of college students were shown an educational video on the importance of exercise, then the number of times the students exercised in the following week was compared to the number of days students at the college exercise per week. It is known that the average number of times per week students at the college exercise is 3.5. Below are data from the group of students who watched the educational video about the importance of exercise. Use this data to answer the question: Does the educational video affect (i.e., cause a difference in) the number of times per week that college students exercise? Times Exercised Per Week Pnum 1 2 3 4 5 6 7 8 9 10 (xm)2 8 5 1 5 4 3 2 3 5 4 M=4 16 1 9 1 0 1 4 1 1 0 34 3.78 1.94 SS s2 s a. What are the independent variable (with the levels) and the dependent variable of the study? b. Step 1: Write the null and research hypotheses in symbols. . c. Calculate the standard error. d. Step 2: Find the critical value for the test statistic? e. Step 3: Find the obtained (i.e., computed) test statistic for a sample (n=10) with a mean of 4. f. Step 4: Make a statistical decision about the null. Will you reject or fail to reject the null based on your sample data? (Be sure to include appropriate test statistic and decision criteria). g. Step 4 (continued): Provide a substantive conclusion about the results from your sample data. (Be sure to include the research context and descriptive statistics). h. Continuing with this example, (i.e. the same population mean, etc.), calculate the effect size of the educational video (those who watched the video compared to those who did not watch the video) on the number of times college students exercise per week (using Cohen's d). How large of an effect size is this, small, medium, or large? 2. You are conducting an experiment to examine whether interpersonal therapy affects symptoms in a sample of war veterans diagnosed with posttraumatic stress disorder (PTSD). A standard measure of PTSD is known to produce a of 20. A sample of 64 war veterans diagnosed with PTSD was given 8 weeks of interpersonal therapy. After the 8 weeks, the sample mean PTSD score was M = 16 and the s = 7. a. What are the independent variable (with the levels) and the dependent variable of the study? b. Step 1: Write the null and research hypotheses in symbols c. Calculate the standard error. d. Step 2: Find the critical value for the test statistic? (Use largest [i.e., most conservative] value if exact value not given in the chart) e. Step 3: Find the obtained (i.e., computed) test statistic for a sample (n=64) with a mean of 16? f. Step 4: Make a statistical decision about the null. Will you reject or fail to reject the null based on your sample data? (Be sure to include appropriate test statistic and decision criteria). g. Step 4 (continued): Provide a substantive conclusion about the results from your sample data. (Be sure to include the research context and descriptive statistics). 3. A researcher designed a study to examine the effect of a new reading program on the number of books read over the summer by 2nd graders. Typically 2nd graders read 3 books over the summer. The researcher recruited a sample of 20 2nd graders and they participated in the new reading program (e.g., they win a prize for every book read over the summer). The researcher wants to know if the new reading program is effective. The following are the number of books read over the summer by students in the new reading program. Attached is the SPSS output. Use the SPSS output to test the question: Does the new reading program affect the number of books read over the summer by 2nd graders? Pnum 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Number of Books Read Over the Summer 4 6 4 10 3 4 2 4 7 5 8 0 4 9 3 1 6 2 5 3 a. What are the independent and dependent variables of the study? b. What are the null and research hypotheses (in symbols)? Below is the output: OneSample Statistics c. From the output above, report the test statistic and the probability (obtained pvalue). Remember to include degrees of freedom when you report tvalues. d. Make a statistical decision about the null using level of significance of .05. Will you reject or fail to reject the null based on the pvalue as computed in the SPSS output? e. Provide a substantive conclusion about the results from your sample data. (Be sure to include the research context and descriptive statistics). f. Compute the r2 effect size. Provide your summary of the effect size (i.e., explain the result in the context of the study) and also indicate if it is small/medium/large. g. How can you tell from the above confidence interval around the difference that there is or is not significance