Over the past few decades, public health officials have...

Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin? The alternative hypothesis is: a. $p<0.30$ b. $p \leq 0.30$ c. $p \geq 0.30$ d. $p>0.30$

Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin? The alternative hypothesis is:
a. $p<0.30$
b. $p \leq 0.30$
c. $p \geq 0.30$
d. $p>0.30$

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population parameter based on sample data. It involves setting up a null hypothesis, which represents the status quo or a specific claim about the parameter, and an alternative hypothesis, which reflects the research interest or claim being tested. The procedure evaluates whether the sample data provide sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

Null and Alternative Hypotheses

In hypothesis testing, the null hypothesis (typically denoted as H?) is a statement that there is no effect or no difference, while the alternative hypothesis (H? or Ha) is what the investigator seeks evidence for. For testing if a proportion exceeds a benchmark value, the null hypothesis usually states that the population proportion is equal to the benchmark, and the alternative hypothesis states that the proportion is greater than the benchmark. This formulation directly guides the testing procedure and interpretation of results.

One-Tailed Test

A one-tailed test is used when the research question is focused on determining whether a parameter is either greater than or less than a specific value, but not both. In this context, since the interest is in finding evidence that more than thirty percent of teen girls smoke to stay thin, the alternative hypothesis is directional (p > 0.30), which results in a one-tailed test. This directs the analysis to only consider deviations in one specified direction.

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