Suppose we to test H0: η = 4.5 vs. Ha: η< 4.5, where η is the population median. Among n= 10 observations, let S be the number of the measurements which are larger than 4.5. Under H0, S follows a binomial(n= 10,p = 0.5).
1) Which of the following sample results gives the strongest evidence to support Ha?
a. S=4
b. S=5
c. S=6
d. They are all the same
2) Following the problem, suppose S = 1, what is the p-value?
a. 0.0010
b. 0.0107
c. 0.9893
d. 0.9990
1)
To support Ha η< 4.5. So, S (the number of the measurements which are larger than 4.5) will be less.
Thus, the lowest value of S will gives the strongest evidence to support Ha
a. S=4
2)
For S = 1, only one of the measurements out of 10 is greater than 4.5
P-value = P(S 1 | S ~ binomial(n= 10,p = 0.5))
= P(S = 0) + P(S = 1)
b. 0.0107
Suppose we are testing Ho: p=.20 vs Ha: p<.20 and TS=2.34. What is the p-value? 0.0096 0.9904 0.0107 0.0192 0.9893 0.0214
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