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.
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.
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