Final answer:
The null hypothesis (H0) is that the population proportion of Americans who prefer to watch news is equal to or greater than 0.50, and the alternative hypothesis (Ha) is that this proportion is less than 0.50. Using the p-value method with a significance level of 0.05, we would calculate the z-test statistic and if the p-value is less than 0.05, we reject H0, supporting the claim.
Step-by-step explanation:
To test the claim that fewer than half of Americans prefer to watch the news rather than read or listen to it, we can set up a hypothesis test using the given information from the poll of 1053 Americans where 47.3% of them indicated this preference. In hypothesis testing, the null hypothesis (H0) represents the status quo or the claim we want to test against, and the alternative hypothesis (Ha) represents the alternative claim. For this scenario:
- H0: p ≥ 0.50 - the population proportion that prefers watching news is equal to or greater than half
- Ha: p < 0.50 - the population proportion that prefers watching news is less than half
We use the p-value method and the normal approximation to the binomial distribution to analyze the data. With a sample proportion of 0.473, a sample size of 1053, and a significance level of 0.05, we would calculate the z-test statistic and compare the resulting p-value to our significance level to decide whether to reject the null hypothesis in favor of the alternative hypothesis. If the p-value is less than the significance level, we would reject the null hypothesis, indicating there is sufficient evidence to support the claim that fewer than half of Americans prefer watching the news.