Question

CareerBuilder.com conducted a survey to learn about the proportion of employers who had ever sent an employee home because they were dressed inappropriately (June \(17,2008,\) www. careerbuilder.com). Suppose you are interested in determining if the resulting data provide strong evidence in support of the claim that more than one-third of employers have sent an employee home to change clothes. To answer this question, what null and alternative hypotheses should you test?

Short answer

The null hypothesis is \(H_0: p = 1/3\) and the alternative hypothesis is \(H_a: p > 1/3\)

Step-by-step solution

Identify the Null Hypothesis

The null hypothesis is a proposition that there is no effect or difference in the population. This is represented as \(H_0\). In this situation, since the question is concerning the claim that more than a third of employers send an employee home to change clothes, the null hypothesis would be that a third or less employers send an employee home to change clothes. Therefore, \(H_0: p = 1/3\), where \(p\) is the proportion of employers who have sent an employee home due to inappropriate dressing.

Identify the Alternative Hypothesis

The alternative hypothesis is a proposition that there is a difference or effect in the population and contrasts with the null hypothesis. This is represented as \(H_a\). Given the claim that more than a third of employers send an employee home to change clothes, the alternative hypothesis would be that more than a third of employers send an employee home to change clothes. Therefore, \(H_a: p > 1/3\)