To determine the type of hypothesis test and the parameter being tested, we need to analyze the given hypotheses:
[tex]\[
\begin{array}{ll}
H_0: & p = 0.1 \\
H_1: & p \neq 0.1
\end{array}
\][/tex]
Here are the steps to identify the test type:
1. Understand the hypotheses:
- The null hypothesis ([tex]\(H_0\)[/tex]) states that the population proportion [tex]\(p\)[/tex] is equal to 0.1.
- The alternative hypothesis ([tex]\(H_1\)[/tex]) states that the population proportion [tex]\(p\)[/tex] is not equal to 0.1.
2. Identify the direction of the alternative hypothesis:
- The alternative hypothesis ([tex]\(H_1\)[/tex]) is [tex]\( p \neq 0.1 \)[/tex]. This means that [tex]\( p \)[/tex] could be either less than or greater than 0.1. It indicates that we are looking for any deviation from the null hypothesis, whether in the positive or negative direction.
3. Determine the test type based on the hypotheses:
- When the alternative hypothesis states that [tex]\( p \)[/tex] is not equal to a certain value (in this case, [tex]\( p \neq 0.1 \)[/tex]), it suggests that we are conducting a two-tailed test. This is because we are interested in deviations in both directions – either smaller or larger than the hypothesized value.
Given the alternative hypothesis [tex]\( H_1: p \neq 0.1 \)[/tex], we conclude that this is a two-tailed test.
4. Identify the parameter being tested:
- The hypotheses revolve around the population proportion [tex]\( p \)[/tex]. Therefore, the parameter of interest in this hypothesis test is [tex]\( p \)[/tex].
Summary:
- The type of test being conducted is a two-tailed test because the alternative hypothesis considers deviations in both directions (greater or smaller than the specified value).
- The parameter being tested in this hypothesis test is the population proportion [tex]\( p \)[/tex].
So the correct answers are:
- Type of test: Two-tailed test
- Parameter tested: [tex]\( p \)[/tex]
