To address the psychologist's claim, we need to set up our hypotheses to reflect the goal of testing whether the true percentage of the population (denoted as [tex]\( p \)[/tex]) that suffers from extreme shyness is greater than 4.1%.
### Step-by-Step Solution
1. Define the null hypothesis (H_0):
- The null hypothesis represents the status quo or the claim that there is no effect or no difference. It is essentially what we assume to be true unless we have strong evidence to suggest otherwise.
- For this problem, the null hypothesis should state that the true percentage of the population suffering from extreme shyness is exactly 4.1%. This hypothesis acts as the benchmark for comparison.
[tex]\[
H_0: p = 4.1\%
\][/tex]
2. Define the alternative hypothesis (H_1):
- The alternative hypothesis represents what we want to test. It is the statement we hope to find evidence for.
- In this case, the psychologist claims that more than 4.1% of the population suffers from extreme shyness. Hence, the alternative hypothesis should reflect a percentage that is greater than 4.1%.
[tex]\[
H_1: p > 4.1\%
\][/tex]
By constructing our hypotheses this way, we set up a scenario where we aim to either reject the null hypothesis in favor of the alternative hypothesis if we find sufficient evidence, or fail to reject the null hypothesis if we do not.
### Conclusion
The correct hypotheses to express the psychologist's claim are:
[tex]\[
\begin{array}{l}
H_0: p = 4.1\% \\
H_1: p > 4.1\%
\end{array}
\][/tex]
