Question

An operator of chocolate-packaging machine monitors the net weights of the packaged boxes by periodically weighing random samples of boxes. One condition required for the proper operation of the machine is that the mean is 453 grams. The operator wishes to see if a random sample of 50 boxes gives evidence that the mean is different than 453 grams. What are the null and alternative hypotheses?

Answer 1

Answer:
`H_0:\mu=453`

`H_1:\mu\\eq453`

Explanation:

Given : An operator of chocolate-packaging machine monitors the net weights of the packaged boxes by periodically weighing random samples of boxes.

The operator wishes to see if a random sample of 50 boxes gives evidence that the mean is different than 453 grams.

i.e. Claim :
`\mu\\eq 453`

We know that the null hypothesis is a kind of claim which always takes equals sign but alternative hypothesis does not.

Thus , the null and alternative hypotheses for the given situation will be :-

`\text{Null hypothesis}\ H_0:\mu=453\\\text{Alternative hypothesis}\ H_1:\mu\\eq453`