Question

a candy company claims that its jelly bean mix contains 15% blue jelly beans. Suppose that the candies are packaged at random in small bags containing about 200 jelly beans. if you receive a bag with 20 blue jelly beans, would you be doubtful of the company claim? answer by calculating the appropriate z-score. Round to the nearest hundredth when necessary.

a. yes, z=9.9

b. no, z=-1.98

c. no, z=1.77

d. yes, z=-1.98

e. yes, z=1.98

Answer 1

H0: p = 0.15

HA: p $\neq$ 0.15

Sample proportion $\hat{p}$ = 20 / 200 = 0.10

Test statistics

z = ($\hat{p}$ - p) / sqrt ( p ( 1 - p) / n )

= (0.10 - 0.15) / sqrt ( 0.15 * 0.85 / 200)

= -1.98

Critical values at 0.05 level = -1.96 , 1.96

Since test statistics falls in rejection region, reject H0.

Yes, z = -1.98