Question

USA Today (March 4, 2010) described a survey of 1,000 women ages 22 to 35 who work full time. Each woman who participated in the survey was asked if she would be willing to give up some personal time in order to make more money. To determine if the resulting data provided convincing evidence that the majority of women ages 22 to 35 who work full time would be willing to give up some personal time for more money, what hypotheses should you test?

Short answer

The null hypothesis (H0) would be \( P \leq 0.5 \), stating that at most half of the surveyed women would be willing to give up personal time for more money. The alternative hypothesis (Ha) would be \( P > 0.5 \), suggesting that more than half of the surveyed women are willing to give up personal time to earn more money.

Step-by-step solution

Formulate Null Hypothesis (H0)

The Null Hypothesis (H0) is the assertion that there is no effect or relationship in the population, implying that the sample observations result purely from chance. In this scenario, it would suggest that at most, half of these women are willing to give up some personal time to make more money. Mathematically, this can be represented as: H0: \( P \leq 0.5 \) , Where P denotes the proportion of women willing to give up personal time for money.

Define the Alternative Hypothesis (Ha)

The Alternative Hypothesis (Ha) would suggest a positive effect or relationship in the sample observations, implying we have enough evidence to reject H0. Thus, Ha would suggest more than half of these women are willing to give up personal time to make more money. This can be represented mathematically as: Ha: \( P > 0.5 \)