Application Problems--t test
1. Seven singers chosen at random single "Jingle Bells" in 58,
60, 68, 63, 59, 64, and 69 seconds. Is the mean time for this song 1 minute?
(alpha equals .05)
2. A physician tests the difference between two kinds of sleep inducing
drugs. Drug A puts a random sample of 8 rats to sleep in a mean time of
7 minutes with a standard deviation of 2 minutes. Drug B puts a random
sample of 10 rats to sleep in a mean of 5 minutes with a standard deviation
of 2 minutes. Is Drug B more effective? (Assume homoscedasticity and alpha
equal .05)
3. A random sample of 12 adult Japanese males have a mean height of 67"
with a standard deviation of 3". A random sample of 12 adult English
males have a mean height of 70" with a standard deviation of 2".
Are adult English males taller than adult Japanese males? (Alpha is equal
to .05).
4. A certain type of X-ray treatment requires an exposure of exactly 10
seconds, it is claimed that a particular X-ray machine does this automatically.
In a random sampling of 10 trials of the machine, the mean exposure time
is 10.2 seconds, with a standard deviation of .7 seconds. Assuming a normal
distribution, is the claim justified at the .05 level of significance?
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