Question

Perchlorate is a chemical used in rocket fuel. People who live near a former rocket-testing site are concerned that perchlorate is present in unsafe amounts in their drinking water. Drinking water is considered safe when the average level of perchlorate is 24.5 parts per billion (ppb) or less. A random sample of 28 water sources in this area produces a mean perchlorate measure of 25.3 ppb. Which of the following is an appropriate alternative hypothesis that addresses their concern? Ha : μ < 25.3 H, a, : , μ, < 25.3 A Ha : μ > 25.3 H, a, : , μ, > 25.3 B Ha : μ < 24.5 H, a, : , μ, < 24.5 C Ha : μ > 24.5 H, a , : , μ, > 24.5 D Ha : μ ≠ 24.5

Answer 1

`H_a > \mu = 24.5`

Explanation:

Given

`n = 28` --- sample size

`\bar x = 25.3` --- Mean

`x = 24.5` --- Average

Required

Determine the alternate hypothesis

From the question, we understand that it is safe to drink water at 24.5 ppb or less.

This implies that the null hypothesis is:

`H_0 \le \mu = \bar x`

i.e.

`H_0 \le \mu = 24.5`

The opposite of
`\le` is
`>`

So, the alternate hypothesis will be:

`H_a > \mu = \bar x`

`H_a > \mu = 24.5`

Hence: (c) is correct