Chapter 11: Q 1. (page 712)

Aw, nuts! A company claims that each batch of its deluxe mixed nuts
contains $52 %$ cashews, $27 %$ almonds, $13 %$ macadamia nuts, and 8% Brazil nuts. To test this claim, a quality-control inspector takes a random sample of $150$ nuts from the latest batch. The table displays the sample data.
a. State appropriate hypotheses for performing a test of the company’s claim.
b. Calculate the expected count for each type of nut.
c. Calculate the value of the chi-square test statistic.

Expert verified

Part (a) $H_{0} : p_{c} = 52 %, p_{a} = 27 %, p_{m} = 13 %, p_{b} = 8 %,$ $H_{a} : A t l e a s t o n e o f t h e p_{i} ’ s i s i n c o r r e c t .$

Part (b)

Part (c) The chi-square test statistic $= 6.60$

Step by step solution

The null and alternative hypotheses:

$H_{0} : p_{c} = 52 %, p_{a} = 27 %, p_{m} = 13 %, p_{b} = 8 %, H_{a} : A t l e a s t o n e o f t h e p_{i} ’ s i s i n c o r r e c t .$

$E x p e c t e d v a l u e = n \times f r e q u e n c y$

Where, $n = 150$

Expected count will be:

Using excel

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