Question

A study measuring fitness level in teens randomly sampled 100 female teens and 102 male teens with a higher score indicating more fitness. Researchers suspected that the fitness level for female teens is lower than for male teens, and wanted to check whether the data would supported this hypothesis. If μ1 and μ2 represent the mean fitness level for female teens and male teens respectively, which of the following is an appropriate pair of hypotheses in this case?A. H0: µ1 − µ2 = 0 Ha: µ1 − µ2 < 0B. H0: µ1 − µ2 < 0 Ha: µ1 − µ2 = 0C. H0: µ1 = µ2 Ha: µ1 > µ2D. H0: µ1 − µ2 = 0 Ha: µ1 - µ2 > 0

Answer 1

`H_0:\mu_1-\mu_2=0`

`H_a: \mu_1-\mu_2<0`

Explanation:

Null hypothesis
`(H_0)` is a statement with shows that there is no statistical difference between the group being tested.

Alternative hypothesis
`(H_a)` is a statement with shows that there is a statistical difference between the group being tested.

Let
`\mu_1` and
`\mu_2` represent the mean fitness level for female teens and male teens respectively.

Given : Researchers suspected that the fitness level for female teens is lower than for male teens, and wanted to check whether the data would supported this hypothesis.

i.e. he wanted to check if
`\mu_1<\mu_2`

Thus , the appropriate pair of hypotheses in this case would be :-

`H_0:\mu_1=\mu_2`

`H_a: \mu_1<\mu_2`

i.e.
`H_0:\mu_1-\mu_2=0`

`H_a: \mu_1-\mu_2<0`