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Activity:
Test for a mean
1. Out
of curiosity, you took your temperature when you felt fine.The
reading was only 97.50.So
you wondered, “Is my average body temperature below 98.60?”To
investigate, you plan to check your temperature on 36 randomly selected
days, and then compute your sample mean.Assume
that your temp’s vary with a standard deviation of s
= 0.80.
(a) Your
research question corresponds to the alternative hypothesis in a hypothesis
test.State this hypothesis in words
and also using symbols.
(b) State
the null hypothesis both in words and symbols.
(c) The
mean that you get from your sample depends on which 36 days you happen
to select.The potential values
for this sample mean vary with a mean of _______, and a standard deviation
of _______ .The potential sample
means form a population that is described by the _________ distribution.
(d) Suppose
you have done the study and got a sample mean of 98.20.What
is the probability of getting a sample mean of 98.20 or lower,
just by chance, if your real mean is 98.60?
(e) The
value of the probability that you calculated above is called the __________.
(f) Many
researchers would consider a probability below _______ as strong enough
evidence to conclude that your average temp. is actually below 98.60.
(g) Does
this probability (e) fall below the value you gave in (f)? _______
(h) Suppose
your sample result was 98.50 (instead of 98.2).Calculate
the probability for this new value as you did in part (d).
(i) Does
this probability (h) fall below the value you gave in (f)? _______