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Potato chips A company that makes potato chips requires each shipment of

potatoes to meet certain quality standards. If the company finds convincing evidence that more than $8\%$of the potatoes in the shipment have 鈥渂lemishes,鈥� the truck will be sent back to the supplier to get another load of potatoes. Otherwise, the entire truckload will be used to make potato chips. To make the decision, a supervisor will inspect a random sample of potatoes from the shipment. He will then perform a test of $H_0:p=0.08$versus $H_a:p>0.08$, where p is the true proportion of potatoes with blemishes in a given truckload. The power of the test to detect that $p=0.11$, based on a random sample of $500$ potatoes and significance level $伪=0.05$, is $0.764$Interpret this value.

Step by step solution

01

Given information

Hypothesized population proportion $\left(p0\right)=0.08$

Sample size $\left(n\right)=500$

Level of significance $\left(伪\right)=0.05$

Power = 0.764

The null and alternative hypotheses are:

$$\begin{gathered} H_0:p=0.08 \\ {H}_a:p>0.08 \end{gathered}$$

02

Concept

The likelihood of rejecting the null hypothesis if the alternative hypothesis is true is defined as the test's power.

03

Explanation

The test's power of $0.764$ indicates that there is a $76.4$ percent chance of concluding that there is adequate evidence to support the alternative hypothesis, $H_0:p>0.08$

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