Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 450 gram setting. It is believed that the machine is underfilling the bags. A 14 bag sample had a mean of 447 grams with a variance of 289. Assume the population is normally distributed. A level of significance of 0.05 will be used. State the null and alternative hypotheses.

Answer 1

`H_0: \mu =450\\\\H_a:\mu<450`

Explanation:

Let
`\mu` be the average weight of potato chips in each bag.

As per given :

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 450 gram setting.

i.e.
`\mu=450`

It is believed that the machine is underfilling the bags.

i.e.
`\mu <450`

• A null hypothesis
  `H_0` is a statement as per the objective of the study which consists of the population parameter like
  `\mu , \sigma , p` etc.

• It believes that there is no such difference between the two groups .

• A alternative hypothesis
  `H_a` is also a statement as per the objective of the study but it is exactly opposite to the null hypothesis .

• It believes that there is statistical difference between the two groups .

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

`H_0: \mu =450\\\\H_a:\mu<450`