Question

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

Answer 1

H0: p = 0.1 and Ha: p > 0.1

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
`H_(0): p = 0.1`

Test if it is more than 10% = 0.1, so the alternate hypothesis is:
`H_(a): p > 0.1`