# Practice Midterm Exam (Statistics)

**Topics:**Standard deviation, Variance, Normal distribution

**Pages:**4 (853 words)

**Published:**January 6, 2012

Instructions: This is a close book exam. Anyone who cheats in the exam shall receive a grade of F. Please provide complete solutions for full credit. Good luck!

1 (for all students in class). In a study of hypnotic suggestion, 5 male volunteers participated in a two-phase experimental session. In the first phase, respiration was measured while the subject was awake and at rest. In the second phase, the subject was told to imagine that he was performing muscular work, and respiration was measured again. Hypnosis was induced between the first and second phases; thus, the suggestion to imagine muscular work was “hypnotic suggestion” for these subjects. The accompanying table shows the measurements of total ventilation (liters of air per minute per square meter of body area) for all 5 subjects.

|Experimental Group | |Subject |Rest |Work | |1 |6 |6 | |2 |7 |9 | |3 |8 |9 | |4 |7 |10 | |5 |6 |7 |

(1) Use suitable test to investigate whether there is any difference between the two experimental phases in terms of total ventilation. Please state the assumption(s) of the test and report the p-value. At the significance level of 0.05, what is your conclusion? (2) Please write up the entire SAS program necessary to answer questions raised in (a). Please include the data step as well as tests for testing for various assumptions.

Solution:

(1) Assume that the difference [pic]is normal.

[pic] and [pic]

The hypotheses are [pic] v.s [pic].

The test statistic is

[pic]

Since [pic] and [pic], we...

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