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. identify the test statistic. z = - 1.65 (round to two decimal places as needed.) identify the p - value. p - value = 0.050 (round to three decimal places as needed.) state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. the null hypothesis. there sufficient evidence to the claim that fewer than half of americans prefer to watch the news rather than read or listen to it.

Explanation:

Step1: State the decision rule for P - value method

In a hypothesis test, if the P - value is less than the significance level \(\alpha\), we reject the null hypothesis. Here, \(\alpha = 0.01\)

Step2: Compare P - value and \(\alpha\)

We are given \(P - value=0.050\) and \(\alpha = 0.01\). Since \(0.050>0.01\) (i.e., \(P - value>\alpha\))

Answer:

Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that fewer than half of Americans prefer to watch the news rather than read or listen to it.