A certain type of flashlight is sold with the four batteries included. A random sample of 150 flashlights is obtained, and the number of defective batteries in each is determined, resulting in the following data:

Number Defective 01234 Frequency 26 51 47 16 10 Let X be the number of defective batteries in a randomly selected flashlight. Test the null hypothesis that the distribution of X is Bin(4, u ). That is, with , test H0: pi 5 a 4

i b ui

(1 2 u)42i i 5 0, 1, 2, 3, 4 pi 5 P(i defectives)

x 5 7, 8, c (x $ 7)

expected cell counts 5 n # (pˆ)x21 # qˆ x 5 1, 2, c pˆ

(gx pˆ i 2 n)/gxi paxi 2n # qn pˆ 5

(px121 # q) # c # (pxn21 # q) 5 n 5 130 p x 5 1, 2, c q 5 1 2 p] x21 # q

[p(x) 5 P(X 5 x) 5 X 5 plausible model for the distribution of the number of borers in a group? [Hint: Add the frequencies for 7, 8, . . . , 12 to establish a single category “ .”]

Number of Borers 0 1 2 3 4 5 6 7 8 9 10 11 12 Frequency 24 16 16 18 15 9 6 5 3 4 3 0 1