Determine whether the claim stated below represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that (a) rejects the null hypothesis or (b) falls to reject the null hypothesis? A scientist claims that the mean incubation period for the eggs of a species of bird is at most 32 days. Does the claim represent the null hypothesis or the alternative hypothesis? Since the claim

To determine whether the claim represents the null hypothesis or the alternative hypothesis, we need to define both hypotheses based on the claim made by the scientist. 1. **Null Hypothesis (H₀)**: This is a statement of no effect or no difference, and it typically represents the status quo or a claim that is being tested. In this case, the null hypothesis would state that the mean incubation period for the eggs of the species of bird is at most 32 days. \[ H_0: \mu \leq 32 \] 2. **Alternative Hypothesis (H₁)**: This is a statement that contradicts the null hypothesis and represents what the scientist is trying to prove. In this case, the alternative hypothesis would state that the mean incubation period is greater than 32 days. \[ H_1: \mu > 32 \] Since the scientist claims that the mean incubation period is at most 32 days, this claim represents the **null hypothesis (H₀)**. ### Interpretation of Decisions in Hypothesis Testing: (a) **Rejecting the Null Hypothesis (H₀)**: If the decision is made to reject the null hypothesis, it suggests that there is sufficient evidence to support the alternative hypothesis. In this context, it would mean that the mean incubation period for the eggs of the species of bird is significantly greater than 32 days. (b) **Failing to Reject the Null Hypothesis (H₀)**: If the decision is to fail to reject the null hypothesis, it indicates that there is not enough evidence to support the alternative hypothesis. In this case, it would mean that the data does not provide sufficient evidence to conclude that the mean incubation period is greater than 32 days, and we would continue to accept the claim that the mean is at most 32 days. In summary: - The claim represents the **null hypothesis (H₀)**. - Rejecting H₀ suggests the mean is greater than 32 days. - Failing to reject H₀ suggests the mean is at most 32 days.