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...

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.
Solution:
a) Null Hypothesis (Ho): There is no correlation between GPA and self-esteem data.
Alternative Hypothesis (Ha): There is correlation between GPA and self-esteem data.
b) Null Hypothesis (Ho): The tax refunds will not create jobs.
Alternative Hypothesis (Ha): The 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:
Solution:
Null Hypothesis (Ho): µ1 = µ2
Alternative Hypothesis (Ha): µ1 ≠ µ2
    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.) 
Solution:
We find the pooled standard deviation,
Sp = √ [(n1 – 1) s1² + (n2 – 1) s2²]/ (n1 + n2 – 2)
= √ [19*(0.026)² + 9*0.047²]/ (20 + 10 – 2)
= √0.001169
= 0.034187
Se = Sp √ (1/n1 + 1/n2) = 0.034187√1/20 + 1/10 = 0.01324
T-statistics = (M1 – M2)/Se
= (0.212 – 0.193)/0.01324
= 1.435
Question 3 of 5
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...