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 researcher claims that the standard deviation of the life of a certain type of lawn mower is more than 2.7 years.
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 standard deviation of the life of a certain type of lawn mower is more than 2.7 years
(b) How should you interpret a decision that fails to reject the null hypothesis?
There is evidence to the claim that the standard deviation of the life of a certain type of lawn mower is more than 2.7 years
(1) Time Remaining: 01:47:50
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Answer
Final Answer: The claim represents the \(\boxed{\text{alternative hypothesis}}\). (a) If we reject the null hypothesis, it means that there is evidence to support the claim that the standard deviation of the life of a certain type of lawn mower is more than 2.7 years. (b) If we fail to reject the null hypothesis, it means that there is not enough evidence to support the claim that the standard deviation of the life of a certain type of lawn mower is more than 2.7 years.
Step 1 ：The claim represents the alternative hypothesis because it is not a statement of no effect or no difference, but a statement that suggests a difference (the standard deviation is more than 2.7 years).
Step 2 ：If we reject the null hypothesis, it means that there is evidence to support the claim that the standard deviation of the life of a certain type of lawn mower is more than 2.7 years.
Step 3 ：If we fail to reject the null hypothesis, it means that there is not enough evidence to support the claim that the standard deviation of the life of a certain type of lawn mower is more than 2.7 years. Instead, we believe that the standard deviation is not more than 2.7 years.
Step 4 ：Final Answer: The claim represents the \(\boxed{\text{alternative hypothesis}}\). (a) If we reject the null hypothesis, it means that there is evidence to support the claim that the standard deviation of the life of a certain type of lawn mower is more than 2.7 years. (b) If we fail to reject the null hypothesis, it means that there is not enough evidence to support the claim that the standard deviation of the life of a certain type of lawn mower is more than 2.7 years.
