State the appropriate null and alternate hypotheses.
Understand the Problem
The question is asking to define the null and alternate hypotheses regarding whether more than 42% of U.S. adults support an internet sales tax based on the provided poll data.
Answer
$$ H_0: p \leq 0.42, \quad H_1: p > 0.42 $$
Answer for screen readers
$$ H_0: p \leq 0.42 $$
$$ H_1: p > 0.42 $$
This hypothesis test is a one-tailed test.
Steps to Solve
- Define the Null Hypothesis
The null hypothesis ($H_0$) states that there is no effect or no difference. In this case, it asserts that the proportion of U.S. adults who support the internet sales tax is equal to or less than 42%. Therefore, we can express it as: $$ H_0: p \leq 0.42 $$
- Define the Alternate Hypothesis
The alternate hypothesis ($H_1$) represents what you are trying to find evidence for. Since the question asks if more than 42% of U.S. adults support the tax, we state this as: $$ H_1: p > 0.42 $$
- Identify the Type of Test
Since we are testing if the proportion is greater than a certain value, this is a one-tailed hypothesis test.
$$ H_0: p \leq 0.42 $$
$$ H_1: p > 0.42 $$
This hypothesis test is a one-tailed test.
More Information
In hypothesis testing, the null hypothesis always reflects a statement of "no effect" or "no difference," whereas the alternate hypothesis is what we suspect might be true. The significance level, usually designated as $\alpha$, helps to determine how strong the evidence must be to reject the null hypothesis.
Tips
- Confusing the null and alternate hypotheses. Always remember: the null hypothesis represents the status quo, while the alternate suggests a change or effect.
- Incorrectly stating the sign for the alternate hypothesis. If the question pertains to “more than,” ensure the alternate hypothesis is correctly written as ( p > \text{value} ).
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