6.4.19. A sample of size 1is taken from the geomctric probability model, px (k) = (1 - p)k-l p, k = 1. 2, 3, . .., to test Ho: p = lversus H1: p > !·The null hypothesis is to be rejected if k .?: 4. What is the probability that a Type II error will be committed when p = 1?
6.4.20. Suppose that one observation from the exponential pdf, f y(y ) = )..e-/..y . y > 0, is to be used to test Ho: " = 1 versus H1 : >.. 1. The decision rule calls for the null hypothesis
to be rejected if y :?:. In 10. Find fJ as a function of "-·
6.4.21. A rnndom sample of size 2 is drawn from a uniform pdf defined over the interval [O, B].
We wish to test
Ho:8 = 2
H1: B 2
by rejecting Ho when YI + Y2 s k . Find the value for k that gives a level of significa nce of0.05.
6.4.22. Suppose that the hypotheses of Question 6.4.21 are to be tested with a decision rule of the form, "Reject Ho: B = 2 if YtY2 ::: k* ." Find the value of k" tha t gives a level of
significance of 0.05 (see Theorem 3.8.3).
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