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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.

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JeanaShupp

Answer:

[tex]H_0: \mu =450\\\\H_a:\mu<450[/tex]

Step-by-step explanation:

Let [tex]\mu[/tex] 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. [tex]\mu=450[/tex]

It is believed that the machine is underfilling the bags.

i.e. [tex]\mu <450[/tex]

  • A null hypothesis [tex]H_0[/tex]  is a statement as per the objective of the study which consists of the population parameter like [tex]\mu , \sigma , p[/tex] etc.
  • It believes that there is no such difference between the two groups .

  • A alternative hypothesis [tex]H_a[/tex] 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 :

[tex]H_0: \mu =450\\\\H_a:\mu<450[/tex]

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