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5 Suppose we assume that the population distribution under Ho is symmetric so that 0; = p.
Without looking at the data to check the validity of this assumption, we apply the binomial
test and the CLT test. Suppose it turns out that 39 data values that are equal to 75.1 and the
40th one is equal to 90.
a What decision is reached using the binomial test to test Ho: 0s= 75 versus He: 05 > 75?
b What decision is reached using the CLT test to test Ho: u = 75 versus H,: u > 75, where
the statistic is computed using the sample standard deviation S in place of the unknown
population standard deviation o?
c Based on the results of parts a and b, what types of distributions that satisfy the alterna-
tive hypothesis are particularly easy for the binomial test to detect in comparison to the
CLT test?
d Replace 90 by other values such as 80, 78, and 76 that are closer to the null hypothesis.
Note what happens to the value of Zy . Does this correspond to intuition?

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