Problem

point(s) possible 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) fails to reject the null hypothesis? A scientist claims that the mean incubation period for the eggs of a species of bird is less than 37 days. Does the claim represent the null hypothesis or the alternative hypothesis? Since the claim a statement of equality, it represents the hypothesis. (a) How should you interpret a decision that rejects the null hypothesis? There is evidence to the claim that the mean incubation period for the eggs of a species of bird is less than 37 days. (b) How should you interpret a decision that fails to reject the null hypothesis? There is evidence to the claim that the mean incubation period for the eggs of a species of bird is less than 37 days.

Solution

Step 1 :The claim represents the alternative hypothesis. This is because the scientist is claiming that the mean incubation period for the eggs of a species of bird is less than 37 days, which is not a statement of no effect or no difference, but a specific claim.

Step 2 :(a) If we reject the null hypothesis, it means that we have found statistically significant evidence to support the alternative hypothesis. In this case, it would mean that we have found evidence to support the scientist's claim that the mean incubation period for the eggs of a species of bird is less than 37 days.

Step 3 :(b) If we fail to reject the null hypothesis, it means that we have not found statistically significant evidence to support the alternative hypothesis. In this case, it would mean that we have not found evidence to support the scientist's claim that the mean incubation period for the eggs of a species of bird is less than 37 days.

Step 4 :Final Answer: The claim represents the \(\boxed{\text{alternative hypothesis}}\). (a) If we reject the null hypothesis, it means that we have found evidence to support the scientist's claim that the mean incubation period for the eggs of a species of bird is less than 37 days. (b) If we fail to reject the null hypothesis, it means that we have not found evidence to support the scientist's claim that the mean incubation period for the eggs of a species of bird is less than 37 days.

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