Suppose the manufacturer of a new drug wants to test H,: 0 = 0.8 versus H,: 0 = 0.6 ere 0 is true proportion of patients cured by the drug. His test statistic is x, the number of cesses (cures) in n = 20 trials, and he will accept Ho if x >16; otherwise he will reject it. nd a and B.

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Chapter1: Combinatorial Analysis
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Q8.
(i) Suppose the manufacturer of a new drug wants to test H,: 0 = 0.8 versus H,: 0 = 0.6
where 0 is true proportion of patients cured by the drug. His test statistic is x, the number of
successes (cures) in n = 20 trials, and he will accept Ho if x >16; otherwise he will reject it.
Find a and ß.
(ii) Now suppose we wish to test Ho: 0 2 0.8 versus H;: 0 < 0.8. Using some selective values
of 0 [ eg 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9] to make a table of the Probabilities of type I error, type
II error and the power function [Probability of rejecting Ho]. Use the table draw a plot of the
power function 1(8).
Transcribed Image Text:Q8. (i) Suppose the manufacturer of a new drug wants to test H,: 0 = 0.8 versus H,: 0 = 0.6 where 0 is true proportion of patients cured by the drug. His test statistic is x, the number of successes (cures) in n = 20 trials, and he will accept Ho if x >16; otherwise he will reject it. Find a and ß. (ii) Now suppose we wish to test Ho: 0 2 0.8 versus H;: 0 < 0.8. Using some selective values of 0 [ eg 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9] to make a table of the Probabilities of type I error, type II error and the power function [Probability of rejecting Ho]. Use the table draw a plot of the power function 1(8).
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