A refrigerator manufacturer claims that the mean life of its competitor's refrigerators is less than 12 years. You are asked to perform a hypothesis test to test this claim. (a) How would you write the null and alternative hypothesis if you represent the manufacturer and want to support the claim? (b) How would you write the null and alternative hypothesis if you represent the competitor and want to reject the claim?
Solution
Step 1 ：Define the null hypothesis (H0) as a statement of no effect, relationship, or difference in our experiment or observation. In this case, the null hypothesis would be that the mean life of the competitor's refrigerators is equal to or more than 12 years.
Step 2 ：Define the alternative hypothesis (H1) as a statement that contradicts the null hypothesis, showing an effect, relationship, or difference. In this case, the alternative hypothesis would be that the mean life of the competitor's refrigerators is less than 12 years.
Step 3 ：If you represent the manufacturer and want to support the claim, write the null and alternative hypothesis as follows: Null Hypothesis (H0): The mean life of the competitor's refrigerators is equal to or more than 12 years. Alternative Hypothesis (H1): The mean life of the competitor's refrigerators is less than 12 years.
Step 4 ：If you represent the competitor and want to reject the claim, write the null and alternative hypothesis as follows: Null Hypothesis (H0): The mean life of the competitor's refrigerators is less than 12 years. Alternative Hypothesis (H1): The mean life of the competitor's refrigerators is equal to or more than 12 years.
Step 5 ：Final Answer: (a) Null Hypothesis (H0): The mean life of the competitor's refrigerators is equal to or more than 12 years. Alternative Hypothesis (H1): The mean life of the competitor's refrigerators is less than 12 years. (b) Null Hypothesis (H0): The mean life of the competitor's refrigerators is less than 12 years. Alternative Hypothesis (H1): The mean life of the competitor's refrigerators is equal to or more than 12 years.
