Question

A candy company claims that 17% of the jelly beans in its spring mix are pink. Suppose that the candies are packaged at random in bags containing about 400 jelly beans. A class of students opens several bags, counts the various colours of jelly beans, and calculates the proportion that are pink. In one bag, the students found 14% of the jelly beans were pink. Is this an unusually small proportion of pink jelly beans? Explain your response.

Answer 1

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.170
sample size       =n=	400
std error of proportion=σp=√(p*(1-p)/n)=	0.0188

therefore P( students found 14% or less of the jelly beans were pink):

probability =

P(X<0.14)

=

P(Z<-1.6)=

0.0548

as above probability is not less than 0.05 level therefore this is not  unusually small proportion of pink jelly beans.