Question

a poll of 1161 americans showed that 46.6% of the respondents prefer to watch the news rather than read or listen to it. use those results with a 0.10 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: Determine the null hypothesis

The null hypothesis \(H_0\) is a statement of equality. Since we are testing against the claim that fewer than half (\(p = 0.5\)) prefer to watch the news, the null hypothesis is \(H_0:p = 0.5\).

Step2: Determine the alternative hypothesis

The alternative hypothesis \(H_1\) is the claim we are testing. The claim is that fewer than half of Americans prefer to watch the news, so \(H_1:p<0.5\).

Answer:

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