Question

A certain television station has been providing live coverage of a particularly sensational criminal trial. The station's program director wishes to know whether more than half the potential viewers prefer a return to regular daytime programming. A survey of randomly selected viewers is conducted. Let \(\pi\) represent the true proportion of viewers who prefer regular daytime programming. What hypotheses should the program director test to answer the question of interest?

Short answer

The null hypothesis \(H_0\) is \(\pi = 0.5\) and the alternative hypothesis \(H_a\) is \(\pi > 0.5\).

Step-by-step solution

Define the Null Hypothesis

The Null Hypothesis, denoted \(H_0\), is a statement about the population that will tested. The null hypothesis for this problem would be: The proportion of viewers who prefer regular daytime programming is equal to half, i.e., \(\pi = 0.5\).

Define the Alternate Hypothesis

The Alternate Hypothesis, denoted \(H_a\) or \(H_1\), is a statement that contradicts the Null Hypothesis. The alternate hypothesis for this problem would be: The proportion of viewers who prefer regular daytime programming is more than half, i.e., \(\pi > 0.5\).