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Q 1.

Expert-verifiedFound in: Page 712

Book edition
6th

Author(s)
Daren Starnes, Josh Tabor

Pages
837 pages

ISBN
9781319113339

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.

Part (a) ${H}_{0}:{p}_{c}=52\%,{p}_{a}=27\%,{p}_{m}=13\%,{p}_{b}=8\%,$ ${H}_{a}:Atleastoneofthe{p}_{i}\u2019sisincorrect.$

Part (b)

Type of nuts | Count | Frequency | Expected |

Cashew | 83 | 52% | 78 |

Almond | 29 | 27% | 40.5 |

Macadamia | 20 | 13% | 19.5 |

Brazil | 18 | 8% | 12 |

Total | 150 | 100% | 150 |

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

Type of nut | Count | Frequency |

Cashew | 83 | 52% |

Almond | 29 | 27% |

Macadamia | 20 | 13% |

Brazil | 18 | 8% |

The null and alternative hypotheses:

${H}_{0}:{p}_{c}=52\%,{p}_{a}=27\%,{p}_{m}=13\%,{p}_{b}=8\%,\phantom{\rule{0ex}{0ex}}{H}_{a}:Atleastoneofthe{p}_{i}\u2019sisincorrect.$

$Expectedvalue=n\times frequency$

Where, $n=150$

Expected count will be:

Type of nuts | Count | Frequency | Expected |

Cashew | 83 | 52% | 78 |

Almond | 29 | 27% | 40.5 |

Macadamia | 20 | 13% | 19.5 |

Brazil | 18 | 8% | 12 |

Total | 150 | 100% | 150 |

Using excel

Type of nuts | Observed | Expected | $O-E$ | ${\left(O-E\right)}^{2}/E$ | % of chisq |

Cashew | 83 | 78.000 | 5.000 | 5.000 | 4.86 |

Almond | 29 | 40.500 | -11.500 | 3.265 | 49.49 |

Macadamia | 20 | 19.500 | 0.500 | 0.013 | 0.19 |

Brazil | 18 | 12.000 | 6.000 | 3.000 | 45.46 |

150 | 150.000 | 0.000 | 6.599 | 100.00 | |

6.60 | chi-square | ||||

3 | Df | ||||

.0858 | p-value |

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