In the context of your example, the null hypothesis \(H_0\) states that the mean battery life is less than 200 hours, and the alternative hypothesis \(H_a\) states that the mean battery life is greater than or equal to 200 hours.
This scenario indicates that you are testing to see if the battery life is significantly greater than 200 hours, which would imply that the sample mean could fall above the claimed value.
Because the focus is on whether the mean battery life is significantly above the specified value of 200 hours, this would be considered a right-tailed test.
- Right-tailed test: This involves testing whether the parameter (in this case, mean battery life, \(\mu\)) is greater than a certain value (200 hours).
In summary:
- \( H_0: \mu < 200 \) (not true)
- \( H_a: \mu \geq 200 \) (this is the hypothesis being tested)
This setup is indicative of a right-tailed test.