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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鈥檚 claim.

b. Calculate the expected count for each type of nut.

c. Calculate the value of the chi-square test statistic.

Short Answer

Expert verified

Part (a)H0:pc=52%,pa=27%,pm=13%,pb=8%,Ha:Atleastoneofthepi鈥�sisincorrect.

Part (b)

Type of nutsCountFrequencyExpected
Cashew8352%78
Almond2927%40.5
Macadamia2013%19.5
Brazil188%12
Total150100%150

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

Step by step solution

01

Part (a) Step 1: Given information

Type of nutCountFrequency
Cashew8352%
Almond2927%
Macadamia2013%
Brazil188%
02

Part (a) Step 2: Explanation

The null and alternative hypotheses:

H0:pc=52%,pa=27%,pm=13%,pb=8%,Ha:Atleastoneofthepi鈥�sisincorrect.

03

Part (b) Step 1: Explanation

Expectedvalue=n脳frequency

Where, n=150

Expected count will be:

Type of nutsCountFrequencyExpected
Cashew8352%78
Almond2927%40.5
Macadamia2013%19.5
Brazil188%12
Total150100%150
04

Part (c) Step 1: Explanation

Using excel

Type of nutsObservedExpectedO-E
O-E2/E
% of chisq
Cashew8378.0005.0005.0004.86
Almond2940.500-11.5003.26549.49
Macadamia2019.5000.5000.0130.19
Brazil1812.0006.0003.00045.46

150150.0000.0006.599100.00







6.60chi-square



3Df



.0858p-value


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