Analyzing Sample of 28 Dumplings: Is Production Standard Met?

[tommyhakinen]

Homework Statement

A dumpling manufacturer selects random sample of 28 dumplings and find that the mean and sample standard deviation are 101 g and 2.5 g respectively.

The production standard of dumplings is to have a 100g. Based on the sample, can manufacture conclude, at 5% level of significant, that the production standard is met? Assume the distribution is normal.

The Attempt at a Solution

Since sigma is not know, t-distribution is used. However, I have problem determining the H1. Is this a one or two tails test? I believe it is a two tails test from this sentence.

The production standard of dumplings is to have a 100g

Any advise? Thanks...

 

[Mark44]

I think you need a one-tailed test, since the standard is (I believe) that the dumplings should not be less than 100 g. IOW, that their weights should be at least 100 g. That's from the customer's perspective. A customer won't care if the dumplings are larger than advertised, but will care if they are smaller.

One could also make the argument that the test should be two-tailed. Although the customer won't mind if the dumplings are larger than the advertised size, the manufacturer would be concerned if they are coming out too large.

Take a look again at the problem wording and see if it offers a clue as to how you should proceed.

 

[Kamkazemoose]

I would assume that you would use a two-tailed test. You want the dumpling to be 100g, and because it doesn't specify a less than or greater than relationship, I would use a two tailed test unless it specifies it being different.