TRY iT Hypothesis A company claims that its tablet computers have an average recharge time of 3 hours, In random the Null is the alternative hypothesis, \( H_{a} \), for this sample of these computers, the average recharge time is 2.5 hours, You suspect that the average recharge time might be less than what the . company claims, Let \( \mu \) represent the average time, in hours, needed to recharge the company's tablet computers. What is the null hypothesis, \( H_{0} \), for this situation? \( \mathbf{x} \mu<3 \)

In hypothesis testing, we set up two competing hypotheses: the null hypothesis (\( H_0 \)) and the alternative hypothesis (\( H_a \)). 1. **Null Hypothesis (\( H_0 \))**: This is the hypothesis that there is no effect or no difference, and it represents the claim that we are testing against. In this case, the company claims that the average recharge time of the tablet computers is 3 hours. Therefore, the null hypothesis can be stated as: \[ H_0: \mu = 3 \] 2. **Alternative Hypothesis (\( H_a \))**: This is what you suspect might be true instead of the null hypothesis. Since you suspect that the average recharge time is less than what the company claims, the alternative hypothesis can be stated as: \[ H_a: \mu < 3 \] In summary: - The null hypothesis \( H_0 \) is that the average recharge time is equal to 3 hours. - The alternative hypothesis \( H_a \) is that the average recharge time is less than 3 hours. Thus, the correct formulation of the hypotheses is: - \( H_0: \mu = 3 \) - \( H_a: \mu < 3 \)