Using StatCrunch to perform hypothesis testing on two independent means of blood pressures

Intro

Howdy!  I’m Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we’re going to learn how to use StatCrunch to perform hypothesis testing on two independent means of blood pressures.  Here’s our problem statement: Assume that the two samples are independent simple random samples selected from normally distributed populations.  Do not assume that the population standard deviations are equal.  Refer to the accompanying data set.  Use a 0.01 significance level to test the claim that women and men have the same mean diastolic blood pressure.

Part 1

OK, the first part of this problem asks us for the null and alternative hypothesis, and it defines mu-1 as the mean diastolic blood pressure for the women and mu-2 as the mean diastolic blood pressure for the men.  Remember that the null hypothesis is always a statement of equality, so answer options A and C are not going to be correct.

Between answer options B and D, we need to look at the alternative hypothesis.  What is the claim that's being made?  Well, the claim that were testing here is that women and men have the same mean diastolic blood pressure.  So the claim is that the two are equal to each other.  But equality by definition belongs to the null hypothesis.  So therefore we have to take the compliment of the claim.  And so if the claim is that they’re equal, the complement of being equal is being not equal to.  So that means we’re going to select answer option B.  Good job!

Part 2

Now the second part of the problem asks us to find the test statistic.  To do this, we’re going to take the data that they give us here, and we’re going to put the data into StatCrunch.  Here’s my window with StatCrunch, and the data is inside.  I'm going to resize this window so we can see a little bit better what's going on.

Alright, so now to get the test statistic, I need to perform the actual hypothesis test.  And the key question of course is “Do we know what the population standard deviation is?”  We’re asked to assume that they're not equal for each of the two groups, but other than that we don't know anything about the population standard deviation.  Therefore, we’re going to use t-scores to calculate our test statistic.

So in StatCrunch, I’m going to go to Stat –> T Stats –> Two Samples (because we have two samples that were comparing) –> With Data (because we have actual data).  Here in the options window, I need to select the columns where my data is located.  Which goes in Sample 1, and which goes in Sample 2?  Well, usually you follow the clue from the problem statement itself.  Here, the women are mentioned first, and the men are mentioned second.  So that’s the order we’re going to put them in here into StatCrunch.  And so the women go first, and then the men go second.

Make sure this box for “Pool variances” is not checked.  It used to be that the default was to check this box, and then they changed the coding in StatCrunch so that the default is now unchecked.  That’s what we want; we want that box unchecked.

Here under “Hypothesis Test,” make sure these values match what you see over here.  And notice the difference in the way that this is expressed.  So here we’re expressing it as a difference.  Here we’re expressing the two statements as being equal to each other.  They’re the same thing.  You just subtract mu-2 from both sides, and you’re going to get the same thing over here.  Not equal to, not equal to — that’s what we want.  I hit Compute! and here in my results window the test statistic is always the second to last number in this table in my results window.  I’m asked to round to two decimal places.  Excellent!

Part 3

And now the third part of this problem asks us to find the P-value.  The P-value is back here in our results window.  It's the last value in the table in the results window.   I’m asked to round to three decimal places.  Fantastic!

Part 4

And  now the last part of this problem asks me to make a conclusion about the null hypothesis and a final conclusion that addresses the original claim.  Well, to do this, we’re just going to take our P-value and compare it with our significance level.  We have a 1% significance level. Here we have a P-value of 35%, which is well above the significance level.  Therefore, we are outside the region of rejection, and therefore we’re going to fail to reject H-naught.  Whenever we fail to reject H-naught, there is not sufficient evidence (or there is insufficient evidence).  And I check my answer.  Well, that’s taking a long time.  Come on, come on, give it to me! Come on!  There we go!  Well done!

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