Question

A machine is supposed to mix peanuts, hazelnuts, cashews, and pecans in the ratio 5:2:2:1. A can containing 500 of these mixed nuts was found to have 269 peanuts, 112 hazelnuts, 74 cashews, and 45 pecans. At the 0.05 level of significance, test the hypothesis that the machine is mixing the nuts in the ratio 5:2:2:1.?

Answer 1

Answer:

the machine is mixing the nuts are not  in the ratio 5:2:2:1.

Step-by-step explanation:

Given that a machine is supposed to mix peanuts, hazelnuts, cashews, and pecans in the ratio 5:2:2:1.

A can containing 500 of these mixed nuts was found to have 269 peanuts, 112 hazelnuts, 74 cashews, and 45 pecans.

Create hypotheses as

H0: Mixture is as per the ratio 5:2:2:1

Ha: Mixture is not as per the ratio

(Two tailed chi square test)

Expected values as per ratio are calculated as 5/10 of 500 and so on

Exp        250      100    100       50        500

Obs       269      112       74       45         500

O-E          19        -12      -26       -5           0

Chi          1.343   1.286  9.135   0.556   12.318

square

df = 3

p value = 0.00637

Since p value < alpha, we reject H0

i.e. ratio is not as per the given