Question

a poll of 1012 americans showed that 47.4% of the respondents prefer to watch the news rather than read or listen to it. use those results with a 0.01 significance level to test the claim that fewer than half of americans prefer to watch the news rather than read or listen to it. use the p - value method. use the normal distribution as an approximation to the binomial distribution.
let p denote the population proportion of all americans who prefer to watch the news rather than read or listen to it. identify the null and alternative hypotheses.
$h_0:p$
$h_1:p$
(type integers or decimals. do not round)

Explanation:

Step1: Understand the claim

The claim is that fewer than half of Americans prefer to watch the news. Half is \(p = 0.5\).

Step2: Set up the null hypothesis

The null hypothesis \(H_0\) is a statement of equality. So \(H_0:p = 0.5\)

Step3: Set up the alternative hypothesis

The alternative hypothesis \(H_1\) is the claim. Since the claim is fewer than half (\(p<0.5\)), so \(H_1:p<0.5\)

Answer:

\(H_0:p = 0.5\)
\(H_1:p<0.5\)