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 H_a). 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 H_oand 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.

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)?

 State your null and alternative hypotheses:

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

1.b. Estimate the p-value for your t-score (using the simplified formula for degrees of freedom k equal to n₁+n₂-2, where n are the sample sizes.) You may do this using the Excel function=tdist(t, d.f., 1 tail)

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?

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?