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CTMG 6006 assignment two questions

Let’s revisit the example data that we presented in Assignment #1. Recall that we were evaluating an
individual’s level of fitness, by measuring the number of liters of oxygen consumed per minute (VO2
max) during a stress test. We obtained the following data (in liters per minute) from a sample of 30
male university students:
52 45 43 56 53 42 54 36 39 51
60 57 49 58 40 45 52 58 44 46
46 51 53 60 44 47 41 38 50 35
and the following data (also in liters per minute) from a sample of 30 female university students:
38 51 35 37 39 43 43 38 51 39
47 41 43 33 42 32 48 48 36 42
45 51 48 37 52 53 34 33 32 38
a) If we wanted to provide male students with an idea as to how many standard deviations their
performance placed them from the mean of other male students, what statistic might we use?
Describe how you might compute this statistic. What statistical value would you provide to a
male student with a VO2 max of 53?
b) Would we calculate different standard score estimates if we standardized to the mean of each
group (as compared to standardizing to the overall mean of both groups)? As an example of
this, present the same standard score, calculated for a woman with a VO2 max of 52,
standardized within the sample of female university students, and then standardized within the
total sample of 60 individuals.
c) If we wanted to present the results in standard scores, but with no negative values, what
standard score would we use? Use this statistic to come up with the standard score for a female
university student with a VO2 max of 48 (normed within the female group).
d) What percentage of the male university student population scores below a male student with a
VO2 max of 53?
e) What percentage of the female university student population scores below a female student
with a VO2 max of 48?
f) Past research has suggested that the average VO2 max in the general population, for males aged
18 to 25, is 44, with a standard deviation of 10. Does our data suggest that our population is
average? Above average? Below average? Justify your conclusion by calculating the probability
of drawing a sample with the descriptive characteristics of our data in male university students.