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Statistics and probability

Course: Statistics and probability > Unit 12

Lesson 1: The idea of significance tests

Writing null and alternative hypotheses

AP.STATS: VAR‑6 (EU), VAR‑6.D (LO), VAR‑6.D.1 (EK), VAR‑6.D.2 (EK), VAR‑6.D.3 (EK), VAR‑6.D.4 (EK), VAR‑6.D.5 (EK), VAR‑7 (EU), VAR‑7.C (LO), VAR‑7.C.1 (EK)

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A ketchup company regularly receives large shipments of tomatoes. For each shipment that is received, a supervisor takes a random sample of 500 tomatoes to see what percent of the sample is bruised and performs a significance test. If the sample shows convincing evidence that more than 10, percent of the entire shipment of tomatoes is bruised, then they will request a new shipment of tomatoes.

Let p represent the proportion of tomatoes in a shipment that are bruised.

What are appropriate hypotheses for the company's significance test?

(Choice A)
$\begin{aligned} &H_0: p = 0.1 \\ &H_\text{a}: p \neq 0.1 \end{aligned}$
(Choice B)
$\begin{aligned} &H_0: p \neq 0.1 \\ &H_\text{a}: p = 0.1 \end{aligned}$
(Choice C)
$\begin{aligned} &H_0: p = 0.1 \\ &H_\text{a}: p > 0.1 \end{aligned}$
(Choice D)
$\begin{aligned} &H_0: p =0.1 \\ &H_\text{a}: p < 0.1 \end{aligned}$

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Statistics and probability

Course: Statistics and probability > Unit 12

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