Final answer:
To determine if more than 40% of U.S. adults favor an internet sales tax, a hypothesis test would be conducted at the 5% significance level using the Gallup poll data. The necessary calculations involve computing the test statistic and comparing it with the critical values or assessing the p-value. The outcome indicates whether there is sufficient evidence to support the claim that more than 40% favor the tax.
Step-by-step explanation:
The Gallup poll asked 1021 U.S. adults whether they believed that people should pay sales tax on items purchased over the internet. Out of these respondents, 459 supported such a tax. To determine if the survey provides convincing evidence that more than 40% of U.S. adults favor an internet sales tax, we will conduct a hypothesis test using the significance level α = 0.05.
Our null hypothesis (H0) is that the true proportion of U.S. adults favoring the tax is 40% or less (π ≤ 0.40), and the alternative hypothesis (H1) is that the true proportion is greater than 40% (π > 0.40). Calculating the test statistic involves computing the standard error of the proportion and then finding the z-score. Once the test statistic is calculated, we can compare it with critical values from the standard normal distribution or use the p-value method to determine if there is enough evidence to reject the null hypothesis.
If the test statistic falls in the critical region or if the p-value is less than the significance level, it indicates that there is significant evidence to support that more than 40% of U.S. adults are in favor of an internet sales tax. Conversly, if the result is not significant, we do not have enough evidence to assert that more than 40% support the tax, but this does not necessarily mean the true proportion is 40% or less, only that our sample does not provide strong evidence to support the claim.