Question

A scientist has come up a new fertilizer for roses. She feels that with the use of this fertilizers, the average blooming time span will increase. But she feels the time span will still be 55 days or more. You don’t agree with the scientist. Which of the following would be the alternative hypothesis to test your belief?

Answer 1

The alternative hypothesis to test the belief that the average blooming time span for a rose will not be at least 55 days is
`\(H_a: \mu < 55\)`.

Explanation: In hypothesis testing, the null hypothesis
`(\(H_0\))` represents the belief you want to challenge, while the alternative hypothesis
`(\(H_a\))` represents the alternative belief. In this case, the scientist believes that the average blooming time span for a rose with the new fertilizer will be at least 55 days. Therefore, the alternative hypothesis to test your belief, which is to disagree with the scientist's claim, would be
`\(H_a: \mu < 55\)`, where
`\(\mu\)` represents the average blooming time span for a rose.

The probable question can be: A scientist has come up a new fertilizer for roses. She feels that with the use of this fertilizers, the average blooming time span for a rose will be at least 55 days? You don’t agree with the scientist. Which of the following would be the alternative hypothesis to test your belief?

Ha: µ > 55

Ha: µ ≥ 55

Ha: µ < 55

Ha: µ ≠ 55