Question 7 of 8 2.0 Points Stating the Research and Null Hypotheses. What you are trying to prove is called the research hypothesis or alternative hypothesis and is symbolized by H1 (some books write it as Ha). Research hypotheses are always expressed in terms of population parameters because we are interested in making statements about a population based on sample statistics. The null hypothesis or H0 contradicts the research hypothesis and is usually a statement of no difference. In each of the following situations state an appropriate null hypothesis Ho and alternative hypothesis H1. Be sure to state it in terms of population parameters. a) An education researcher believes that among college students there is a correlation between grade point average (GPA) and self-esteem data. b) The President believes that tax refunds will create jobs. Question 1 of 5 1.0 Points The Manager of the Toledo Mudhens decides to see whether batting practice (think of this as the equivalent a week long series of professional development seminars) has any impact. Twenty Mudhens take batting practice; they are a randomly selected experimental group. Ten Mudhens randomly selected take no batting practice (control group). After 30 games the figures shown in the accompanying table are available. What can you tell the manager about his experiment statistically and managerially (i.e. practically)? Batting Practice Group No-Practice Group Mean .212 .193 Standard Deviation .026 .047 Sample Size (n) 20 10 State your null and alternative hypotheses: Question 2 of 5 2.0 Points 1a. Using data from the question above calculate your t-score – which involves first calculating the standard of error for the difference (see formulas in your text; is this a paired or independent sample?; assume unequal variance.) Question 3 of 5 1.b. Estimate the p-value for your t-score (using the simplified formula for degrees of freedom kequal to n1 n2-2 where n are the sample sizes.) You may do this using the Excel function=tdist(t d.f. 1 tail) Question 4 of 5 2.0 Points 1c. Is the difference of means statistically different from zero? Is it practically different from zero? In other words what can you tell the manager about this experiment? Should s/he institute the new batting practice procedure? Question 5 of 5 3.0 Points 2. A supervisor in the Department of Rehabilitive Services is critical of the performance of one of her counselors. The counselor is expected to arrange job training for those in need of vocational rehabilitation so that they may find employment. Yet the counselor has managed to place just 35% of his clients. The counselor argues that he is doing a good job and that the reason for his overall low rate of placement is that most of his clients are severely disabled which makes them very difficult to place. The counselor’s case load is presented in the accompanying table. Percentage the table appropriately and evaluate who is correct — the supervisor or the counselor? Job Placement Not Severely Disabled Severely Disabled Not Placed 17 118 Placed 47 26 Question 1 of 4 1.0 Points You have been given sample data from two offices and told that the 95% confidence interval for the difference of mean in overtime hours per year is -.01 to 100. What can you say about the difference in average overtime hours for each office? A. Overtime hours are statistically significant at alpha=.05 B. Overtime hours are not statistically significant at a 95% confidence level. C. Overtime hours are practically significant. D. We can’t tell from the data. Question 2 of 4 1.0 Points What if I told you in Q1 above that the sample sizes were n=20 and n=30 for each office what would you say then? A. A sample size of 30 is the minimum sample size to make the law of large numbers work so we cannot draw conclusions from this data. B. Use a t-score for the smaller sample and a z-score for the larger one. C. If the sample sizes were increased we would likely see a statistically significant difference at the 95% confidence level. D. A and C E. B and C Question 3 of 4 1.0 Points You have conducted a pilot study of a new initiative to improve employee morale using experimental design on samples of employees and you have found that in a regression equation morale has improved by 2 points out of 10 with a p-value of .07. What can you say about your pilot study? A. The t-score for my regression coefficient is likely less than 2. B. My regression coefficient does not meet standards for statistical significance and on that basis I cannot draw firm conclusions about my innovation. C. This is a pilot study so I can draw some tentative conclusions about my innovation. D. A and C. E. All of the above. Question 4 of 4 1.0 Points For the 4 examples below comparing Boys’ and Girls Mean Test Scores match the example to the proper qualitative description. A. Could be large important difference but we have no idea. Not enough data to tell. B. Lots of data make small unimportant difference statistically significant. C. We’re sure that there is no difference of a magnitude large enough to matter. D. An important difference that’s really there. 1. Example A Sample Size 10 000 Overall Mean 200 Std. Dev. 25 Girls’ Mean Score 175 Boys’ Mean Score 225 Difference in Score 50 Standard Error of the Difference =2xSD/sqrt(10 000) =2×25/sqrt(10 000) =.5 t-score and p-value t = 100 p < .0001 2. Example B Sample Size 10 000 Overall Mean 200 Std. Dev. 25 Girls' Mean Score 199 Boys' Mean Score 201 Difference in Score 2 Standard Error of the Difference =2xSD/sqrt(10 000) =2x25/sqrt(10 000) =.5 t-score and p-value t = 4 p < .001 3. Example C Sample Size 9 Overall Mean 200 Std. Dev. 100 Girls' Mean Score 175 Boys' Mean Score 225 Difference in Score 50 Standard Error of the Difference =2xSD/sqrt(9) =2x100/sqrt(9) =66.6 t-score and p-value t = .75 p > .40 4. Example D Sample Size 1 000 Overall Mean 200 Std. Dev. 25 Girls’ Mean Score 199 Boys’ Mean Score 201 Difference in Score 2 Standard Error of the Difference =2xSD/sqrt(1 000) =2×25/sqrt(1 000) =1.58 t-score and p-value t = 1.26 p > .20
