Question

identify the correct null and alternative hypotheses.
a hypnosis program designed to help individuals quit smoking claims a 57% success rate. a consumer watch group suspects that this claim is high and randomly selects 50 individuals who have completed the program in order to conduct a hypothesis test. what are the appropriate null and alternative hypotheses?
$h_0: p = 0.57$ vs. $h_a: p < 0.57$
$h_0: p = 0.57$ vs. $h_a: p > 0.57$
$h_0: p = 0.57$ vs. $h_a: p ≠ 0.57$
$h_0: p < 0.57$ vs. $h_a: p > 0.57$

Explanation:

Step1: Understand the null hypothesis concept

The null hypothesis \(H_0\) is a statement of no effect or no difference. Here, the claim is a 57% success rate, so \(H_0: p = 0.57\).

Step2: Understand the alternative hypothesis concept

The consumer - watch group suspects the claim is high. So the alternative hypothesis \(H_a\) is that the proportion \(p\) is less than 0.57, i.e., \(H_a: p<0.57\).

Answer:

\(H_0: p = 0.57\) vs. \(H_a: p<0.57\)