Question

express the null hypothesis and the alternative hypothesis in symbolic form. use the correct symbol ($\mu$, $p$, $\sigma$) 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.
oa. $h_0: p < 5.8%$
$h_1: p \geq 5.8%$
ob. $h_0: p > 5.8%$
$h_1: p < 5.8%$
oc. $h_0: p = 5.8%$
$h_1: p > 5.8%$
od. $h_0: p = 5.8%$
$h_1: p < 5.8%$

Explanation:

Step1: Understand null and alternative hypotheses

The null hypothesis \(H_0\) is a statement of no - effect or equality. The alternative hypothesis \(H_1\) is the claim we are trying to find evidence for.

Step2: Analyze the claim

The claim is “more than 5.8%”. The null hypothesis for a proportion \(p\) (when the claim is about a proportion) is usually a statement of equality. So \(H_0:p = 5.8\%\). The alternative hypothesis for “more than” is \(H_1:p>5.8\%\)

Answer:

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