Question
The mean weight of male aerobics instructors in a certain city is at least 164 lbs. Express the null and alternative hypotheses in symbolic form for this claim.
Answers
GPT-4o mini
To express the null and alternative hypotheses symbolically for the claim that the mean weight of male aerobics instructors in a certain city is at least 164 lbs, we can denote the population mean weight by \(\mu\).
The null hypothesis (\(H_0\)) represents the claim that is initially assumed to be true, while the alternative hypothesis (\(H_a\)) represents the claim we want to test.
1. **Null Hypothesis (\(H_0\))**: \(\mu \geq 164\) (the mean weight is at least 164 lbs)
2. **Alternative Hypothesis (\(H_a\))**: \(\mu < 164\) (the mean weight is less than 164 lbs)
In summary:
- \(H_0: \mu \geq 164\)
- \(H_a: \mu < 164\)
The null hypothesis (\(H_0\)) represents the claim that is initially assumed to be true, while the alternative hypothesis (\(H_a\)) represents the claim we want to test.
1. **Null Hypothesis (\(H_0\))**: \(\mu \geq 164\) (the mean weight is at least 164 lbs)
2. **Alternative Hypothesis (\(H_a\))**: \(\mu < 164\) (the mean weight is less than 164 lbs)
In summary:
- \(H_0: \mu \geq 164\)
- \(H_a: \mu < 164\)