Hypothesis test - finding the right hypothesis

ISTER_REG

ISTER_REG

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I have a question concerning, how to find the right hypothesis onto this question:

A company supplies plastic sheets for industrial use. A new type of plastic has been produced and the company would like to claim that the average stress resistance of this new product is at least 30.0, where stress resistance is measured in pounds per square inch (psi) necessary to crack the sheet. The following random sample was drawn off the production line. Based on this sample, would the claim clearly be unjustified? 30.1 32.7 22.5 27.5 27.7 29.8 28.9 31.4 31.2 24.3 26.4 22.8 29.1 33.4 32.5 21.7 Assume normality and use the 5 percent level of significance.

Based on the sentence "company would like to claim", I would say that this speaks for an alternative hypothesis e.g. [MATH]H_1: \mu > \mu_0[/MATH], because in this one we are making an assumption. It is said that the "company would like to claim" not "company claims that...". In fact, the following alternative hypothesis is used in the solution [MATH]H_1: \mu < \mu_0[/MATH] , why is this, what is the evidence for it?

The calculation is not the problem now, but rather the linguistic understanding...
 
ISTER_REG said:
I have a question concerning, how to find the right hypothesis onto this question:

A company supplies plastic sheets for industrial use. A new type of plastic has been produced and the company would like to claim that the average stress resistance of this new product is at least 30.0, where stress resistance is measured in pounds per square inch (psi) necessary to crack the sheet. The following random sample was drawn off the production line. Based on this sample, would the claim clearly be unjustified? 30.1 32.7 22.5 27.5 27.7 29.8 28.9 31.4 31.2 24.3 26.4 22.8 29.1 33.4 32.5 21.7 Assume normality and use the 5 percent level of significance.

Based on the sentence "company would like to claim", I would say that this speaks for an alternative hypothesis e.g. [MATH]H_1: \mu > \mu_0[/MATH], because in this one we are making an assumption. It is said that the "company would like to claim" not "company claims that...". In fact, the following alternative hypothesis is used in the solution [MATH]H_1: \mu < \mu_0[/MATH] , why is this, what is the evidence for it?

The calculation is not the problem now, but rather the linguistic understanding...
Click to expand...
The claim, which they want to support (and thus be able to make publicly) is "the average stress resistance of this new product is at least 30.0". This does not mean "greater than"; it means "greater than or equal to".

Since this includes equality, this is taken as the null hypothesis, and the alternative hypothesis is the negation of \(\mu\ge 30\), namely \(\mu\lt 30\).

You're right, the issue is largely linguistic, though "would like to" is not the issue.

(Also, frankly, as a non-statistician, I am a little suspicious of the simplicity of the explanation I've just given, based on what I find in textbooks, that whether a claim happens to include equality is sufficient to determine all of this.)
 
Thanks for the answer! I must admit, your approach to see the "equal" in the symbol/statement is really clever! That's a good tip to use.
 
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