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 matched pair means. Here's our problem statement: The accompanying table lists the attribute ratings made by a random sample of participants in a speed-dating session. Each attribute rating is the sum of the ratings of five attributes: sincerity, intelligence, fun, ambition, shared interests. Use a 0.05 significance level to test the claim that there is a difference between female attribute ratings and male attribute ratings.
OK, this first part of a problem is asking us to identify the null and alternative hypotheses. For matched pair means, the parameter that we look at is the difference from the population mean, so we identify that with use of d (subscript). This is our population parameter for our hypotheses.
The null hypotheses is by definition a statement of equality, so it will always be that the parameter is equal to some value. Here we're actually looking at matched pair mean differences. And when you're looking at differences, typically the value that you're looking at is zero.
The alternative hypothesis — let's see if we can match the claim. The claim here is that there's a difference between female attribute ratings and male attribute ratings, so there's some difference. So it could be that the female is greater than the male, or the female is less than the male. It doesn't matter which side you're on; it's just one or the other. And if you're on either side, there's some difference there. That means we have a two-sided test, and this is going to be, therefore, not equal to (again, the same value) zero. Nice work!
The next part asks us to identify the test statistic. To do this, I'm gonna let StatCrunch do the heavy lifting for me. So here's my data. I click on this icon so I can dump the data into StatCrunch. And now my data is in StatCrunch. I’m going to resize this window so we can see more what's going on.
And now in StatCrunch, I'm gonna go to Stat –> T Stats –> Paired. In the options window, I’m going to tell StatCrunch where to find my data. Notice with the paired sample option, I don't have the ability to do the test with anything but actual data. So I can't provide summary statistics in order to do the test; I have to have actual data. That's just part of the way that the software was coded. We actually do have actual data, so it's not a big problem.
You need to select the samples and put them or tell StatCrunch where the data is actually going to be located. So typically you're going to just take the column listed first as the first sample and the one that's listed next as the second sample. Then down here under Perform, we're going to select the radio button for hypothesis test. This is the default selection, so it's already done for us. And the default selections here already match the null and alternative hypothesis for our particular situation, so we don't need to make any changes to the default values here. If there were changes needed, then we could make them. We want to make sure that these fields here match the null internal hypothesis for our particular situation.
Once you get that matched up, there's nothing else to do. So just press Compute! and in the results window here on the end of the table is your test statistic. I'm asked to round to two decimal places. Fantastic!
The next part asks us to identify the P-value. The P-value is right here in the same table in the results window next door to the test statistic. It's the last value in the table. I'm asked to round to three decimal places. Fantastic!
And now the last part of the problem asks us to make a conclusion on the hypothesis test. First, one thing we need to do is compare the P-value with a significance level. We were given a significance level of 5% here in the problem statement. Our P-value is way more than 5%; we're almost at 88%, so we're definitely greater than 5%. So the P-value is greater than the significance level. Because the p-value is greater than the significance level, we are outside the region of rejection, and therefore we're going to fail to reject the null hypothesis. And because we fail to reject the null hypothesis, there is not sufficient evidence. I check my answer. Fantastic!
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Frustrated with a particular MyStatLab/MyMathLab homework problem? No worries! I'm Professor Curtis, and I'm here to help.