Question

A certain manufactured product is supposed to contain 23.2% potassium by weight. A sample of 10 specimens of this product had an average percentage of 23.6 with a standard deviation of 0.3. If the mean percentage is found to differ from 23.2, the manufacturing process will be recalibrated. State the appropriate null and alternate hypotheses.

Answer 1

The null hypothesis is
`H_0: \mu = 23.2`

The alternate hypothesis is
`H_a: \mu \\eq 23.2`

Explanation:

Null hypothesis:

The product is supposed to contain 23.2% potassium by weight, which means that at the null hypothesis, we test that this is the correct weight. So

`H_0: \mu = 23.2`

Alternate hypothesis:

If the mean percentage is found to differ from 23.2, the manufacturing process will be recalibrated, which means that we test if the mean differs from 23.2, that is:

`H_a: \mu \\eq 23.2`