Let's break down the problem step by step. Here's the information provided:

1. Context: A survey asked 1017 U.S. adults about their support for an internet sales tax, and 397 supported the tax.
2. Claim: Determine if more than 38% of U.S. adults support the tax (claim: $p > 0.38$).
3. Significance Level: $\alpha = 0.01$.
4. Hypotheses: We need to establish the null and alternative hypotheses.

Step (a): State the null and alternate hypotheses

• Null Hypothesis ($H_0$): The proportion of U.S. adults supporting the tax is equal to 38%. Mathematically: $H_0: p = 0.38$

• Alternative Hypothesis ($H_1$): More than 38% of U.S. adults support the tax. Mathematically: $H_1: p > 0.38$

This is a right-tailed test because the claim is that the true proportion $p$ is greater than 0.38.

Would you like me to proceed with calculating the test statistic and $p$-value, or provide further explanation of these hypotheses? Let me know!

Follow-Up Questions

1. How is the decision between a right-tailed, left-tailed, or two-tailed test determined?
2. What formula is used to calculate the test statistic for a population proportion?
3. How does the significance level ($\alpha$) influence the interpretation of the results?
4. How can the TI-84 Plus calculator be used to compute the $p$-value?
5. What does it mean if the $p$-value is less than the significance level?

Tip:

Always clearly distinguish between the null hypothesis ($H_0$) and the alternative hypothesis ($H_1$), as they form the foundation for hypothesis testing.