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.

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Answer:

The null hypothesis is [tex]H_0: \mu = 23.2[/tex]

The alternate hypothesis is [tex]H_a: \mu \neq 23.2[/tex]

Step-by-step 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

[tex]H_0: \mu = 23.2[/tex]

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:

[tex]H_a: \mu \neq 23.2[/tex]