Question 22 of 22 (t.9 points) I Question Attempt: 1 of 3 Kne Television Set Ownership According to Nielsen Media Research, of all the U.S. households that owned at least one television set, \( 83 \% \) had two or more sets. A local cable company canvassing the town to promote a new cable service found that of the 299 households visited, 221 had two or more television sets. At \( \alpha=0.10 \), is there sufficient evidence to conclude that the proportion is less than the one in the report? Do not round intermediate steps. Part: \( 0 / 5 \) Part 1 of 5 (a) state the hypotheses and identify the claim. \[ \begin{array}{l} H_{0}=\square(\text { Choose one) } \mathbf{V} \\ H_{1}=\square(\text { Choose one }) \mathbf{V} \end{array} \] This hypothesis test is a \( \square \) (Choose one) test. \( \square \)

To solve this problem, we need to set up the hypotheses for a hypothesis test regarding the proportion of households with two or more television sets. ### Step 1: State the Hypotheses 1. **Null Hypothesis (\(H_0\))**: This is the hypothesis that there is no effect or no difference. In this case, we want to test if the proportion of households with two or more television sets is equal to the reported proportion of \(83\%\) (or \(0.83\)). \[ H_0: p = 0.83 \] 2. **Alternative Hypothesis (\(H_1\))**: This is the hypothesis that there is an effect or a difference. Since we want to determine if the proportion is less than the reported proportion, we will set up the alternative hypothesis as: \[ H_1: p < 0.83 \] ### Step 2: Identify the Claim The claim is that the proportion of households with two or more television sets is less than \(83\%\). Therefore, the claim corresponds to the alternative hypothesis \(H_1\). ### Step 3: Identify the Type of Test This hypothesis test is a **one-tailed test** because we are only interested in whether the proportion is less than the reported value. ### Summary Putting it all together, we have: \[ \begin{array}{l} H_{0}: p = 0.83 \\ H_{1}: p < 0.83 \end{array} \] This hypothesis test is a **one-tailed test**.