Chapter 11.1, Problem 1E

(a)

To determine

To state: the hypotheses for performing a test of company’s claim that each batch of its deluxe mixed nuts contains 52% cashews, 27% almonds, 13% macadamia and 8% brazil nuts whereas a random sample of 150 nuts from each batch is having the following composition.

Nut	Cashew	Almond	Macadamia	Brazil
count	83	29	20	18

Answer to Problem 1E

The null hypothesis will be H₀: The observed count of each type of nuts in a group of 150 nuts from latest batch are same as claimed count of nuts in a group of 150.

Versus

H₁: The observed counts of each type of nuts in a group of 150 nuts from latest batch are not same as claimed count of nuts in a group of 150.

Explanation of Solution

The null hypothesis will be H₀: The observed count of each type of nuts in a group of 150 nuts from latest batch are same as claimed count of nuts in a group of 150.

Versus

H₁: The observed counts of each type of nuts in a group of 150 nuts from latest batch are not same as claimed count of nuts in a group of 150.

Since proportion of nuts of each type as per the claim is for 100, we can obtain the proportion of each type of nuts in 150 by multiplying by each number by 150.

(b)

To determine

To find: expected counts of nuts of each type in a group of 150.

Answer to Problem 1E

The expected count of nuts is given in the table below.

  

Explanation of Solution

Since proportion of nuts of each type as per the claim is for 100, we can obtain the proportion of each type of nuts in a group of 150 by multiplying by each count by 150.