Question.

Forty-five participants (15 per group) were randomly assigned to perform series of math tasks while listening to soft-gentle music, while listening to loud-intense music, or while in silence.

The means and estimated population variances for the three groups were: Soft-Gentle: M = 37, S2 = 28

Loud-Intense: M = 33, S2 = 25

Silence: M = 41, S2 = 22

Using the .05 significance level, is there a difference in performance on this kind of math task under these three conditions?

a. Use the five steps of hypothesis testing.

Describe the populations and restate the question as a research hypothesis and a null hypothesis (6 pts.).

Determine the characteristics of the comparison distribution (8 pts.).

dfbetween =

dfwithin =

Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. Find your cutoff score on the F table using the appropriate numerator df and a denominator df of 40 .

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4. Determine your sample's score on the comparison distribution .

GM=

S2M=

S2Between =

S2Within =

F=

Decide whether to reject the null hypothesis.

b. Figure the effect size for this study and indicate whether it is nearer to small, medium, or large (5 pts.). 1. R2=

c. Conduct a planned contrast for the Soft-Gentle versus Silence conditions (using the .05 level). 1. What is your new cutoff score on the F distribution (using a denominator df of 40)?

2. GM=

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S2Between =

S2Within (the exact same S2Within as your overall ANOVA) =

5. F=

6. Decide whether to reject the null hypothesis.

7. Conduct Scheff's test (using the F value you figured from your planned contrast) and indicate the F cutoff, the F you would use for the comparison, and the hypothesis-testing decision (reject or do not reject).

Suppose Xn is a two-state Markov chain whose transition probability matrix is P = 1-B B Then, Zn = (Xn-1, Xn) is a Markov chain having the four states (0,0), (0,1), (1,0), and (1,1). Determine the transition probability matrix.6. A Markov chain with the states 1, 2, 3 has transition probability matrix: 1 . P: 2 0.4 0.3 b 3 (a) Give the values of a, b, and c that make the above a valid transition probability matrix. (3 points) Example: Shopping Mall Renovation Activity A: Prepare initial design B: Identify new potential clients C: Develop prospectus for tenants D: Prepare final design U minmONmy IITTOWOO E: Obtain planning permission On NHAMInHAM OATNHANHOH F: Obtain finance from bank G: Select contractor H: Construction LUI WU I: Finalize tenant contracts J: Tenants move in I H SEEM 3530 PERTEstimation of the activity duration Three key values we use in the time estimate for each activity: a = optimistic time, which means that there is little chance that the activity can be completed before this time; c = most likely time, which will be required if the execution is normal; b = pessimistic time, which means that there is little chance that the activity will take longer