When peanuts are packaged in their shells, most shells have two peanuts inside, but some have three and some only have one. A quality control inspector wants to determine if more than 10% of all shells contain just one peanut. If the inspector were to conduct a hypothesis test for p, the proportion of shells with just one peanut, what would be the appropriate pair of hypotheses for the inspector to use? H0: p = 0.1 and Ha: p ≠ 0.1 H0: p = 0.1 and Ha: p < 0.1 H0: p = 0.1 and Ha: p > 0.1 H0: p < 0.1 and Ha: p > 0.1 H0: p > 0.1 and Ha: p = 0.1

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01-04-2021
Mathematics

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When peanuts are packaged in their shells, most shells have two peanuts inside, but some have three and some only have one. A quality control inspector wants to determine if more than 10% of all shells contain just one peanut. If the inspector were to conduct a hypothesis test for p, the proportion of shells with just one peanut, what would be the appropriate pair of hypotheses for the inspector to use? H0: p = 0.1 and Ha: p ≠ 0.1 H0: p = 0.1 and Ha: p < 0.1 H0: p = 0.1 and Ha: p > 0.1 H0: p < 0.1 and Ha: p > 0.1 H0: p > 0.1 and Ha: p = 0.1

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joaobezerra joaobezerra · Answer 1 · 2021-04-02T21:17:26-04:00

Answer:

H0: p = 0.1 and Ha: p > 0.1

Step-by-step explanation:

At the null hypothesis, we test if the mean or proportion is equal to a certain value.

At the alternate hypothesis, we test if the mean or proportion is less than, more than, or different of the value tested at the null hypothesis.

A quality control inspector wants to determine if more than 10% of all shells contain just one peanut.

The value of 10% = 0.1 is tested, which means that the null hypothesis is [tex]H_{0}: p = 0.1[/tex]

Test if it is more than 10% = 0.1, so the alternate hypothesis is: [tex]H_{a}: p > 0.1[/tex]

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