Identifying the symbolic claim and hypotheses for a claim about a population standard deviation

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to identify the symbolic claim and hypotheses for a claim about a population standard deviation.  Here's our problem statement: Claim: The standard deviation of pulse rates of adult males is more than 12 bpm for a random sample of 161 adult males.  The pulse rates of a standard deviation of 12.8 bpm. Complete Parts A and B below.

Part A

OK, Part A asks us to express the symbolic form of the original claim.  So to do that, we first look in our problem statement to see where the claim is.  The claim is this first statement here in the problem statement: "The standard deviation of pulse rates of adult males is more than 12 beats per minute."  So [in] this first dropdown, we want to select the population parameter that matches standard deviation.  It's not going to be the p because p is the representation for population proportion.  It's not going to be μ because μ is the representation for population mean. What we want is σ; σ is the population standard deviation.  So this is what we'll select.

And then in the next dropdown, we want to look and see what does the claim say about which inequality symbol we should be using.  Here it says standard deviation is more than 12, so we want to select greater then.  And then our claimed value is that value from the claim, which is 12.  I check my answer.  Good job!

Part B

Now Part B wants us to identify the null and alternative hypotheses.  These hypotheses will always use the same population parameter from what we see here earlier in Part A.  So we're looking at standard deviation, so I'm going to select that here.  The null hypothesis is by definition a statement of equality.  So I want to select the equal sign.  And then this value is the claimed value, which we saw earlier was 12.  There's my null hypothesis.

The alternative hypothesis --- typically the alternative hypothesis reflects the claim unless there is some semblance of equality with the claim, because equality by definition belongs to the null hypothesis.  So if there's any semblance of equality with the claim, then we have to take the compliment for our alternative hypothesis.  Here, if we look here to Part A, what we have here --- notice how the symbol here is greater than.  There's no or equal to; there's no semblance of equality here.  So therefore we can just adopt this statement as our alternative hypothesis.  Nice work!

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