Question

express the null hypothesis and the alternative hypothesis in symbolic form. use the correct symbol (μ, p, σ) for the indicated parameter.
a psychologist claims that more than 5.8% of the population suffers from professional problems due to extreme shyness. use p, the true percentage of the population that suffers from extreme shyness.
a. h₀: p = 5.8%
h₁: p > 5.8%
b. h₀: p = 5.8%
h₁: p ≤ 5.8%
c. h₀: p = 5.8%
h₁: p ≥ 5.8%
d. h₀: p = 5.8%
h₁: p < 5.8%

Explanation:

• The null hypothesis \(H_0\) is a statement of equality. Here, it is \(p = 5.8\%\) as we assume no difference initially.
• The alternative hypothesis \(H_1\) is what the psychologist is claiming. Since the claim is "more than 5.8%", the alternative hypothesis is \(p>5.8\%\).

Answer:

A. \(H_0: p = 5.8\%\), \(H_1: p>5.8\%\)