Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to perform Spearman's rank correlation test for audience impressions. Here's our problem statement: The table below lists the numbers of audience impressions in hundreds of millions listening to songs and the corresponding numbers of albums sold in hundreds of thousands. Does it appear that album sales are affected very strongly by the number of audience impressions? Use the significance level of alpha equals 0.05.
OK, the first part of this problem is asking for null and alternative hypotheses and for a rank correlation test. That's pretty much going to be set. The null hypothesis is going to say there is no correlation, so it's going to be equal to zero. And the alternative will be that there is correlation, so the correlation coefficient will not be equal to zero. We want to get a population parameter because we always use population parameters with our null and alternative hypotheses. So we don't want to choose a sample statistic, and that means we're going to select this answer option here. Nice work!
Now the next part asks us to find the value of the correlation coefficient. To do that, we're going to take our data and dump it into StatCrunch. OK, here we are in StatCrunch. And now I'm going to go to Stat --> Nonparametrics --> Spearman's correlation. Here in my options window, I'm going to select the columns where my data can be found, and I'm just going to hit Compute!, and here it is. There's my correlation coefficient. Notice the negative sign out in front. We want to be sure to include that. Fantastic!
Now the next part asks for critical values, and critical values are obtained from a table where we've got less than 30 for sample size. And here we definitely have less than 30 for sample size. So n is equal to 9. So we've got nine sample pairs, and we're asked to use the significance level of 5%. So if I look on the table here for sample size of 9 and 5%, I'm going to get 0.7. So I've got two critical values, so I'm going to use my plus or minus sign so I only have to type the number in once. Well done!
And now the last part asks us to resolve the hypothesis test. Well, here we've got a test value --- a test statistic, rather, of -0.181, and that's going to be between 0.7 and -0.7. So therefore we're outside the region of rejection, and we're going to fail to reject the null hypothesis. And every time we fail to reject the null hypothesis, there's insufficient evidence. But that's not how these are worded here. So let's see what we got. Yeah, this one says there appears to be a correlation between the number of audience impressions and the number of albums sold. And this one says there does not appear to be a correlation. So which is it?
Well, we failed to reject the null hypothesis, which means it's potentially true. And here the null hypothesis says there is no correlation. So it's potentially true that there is no correlation. So there does not appear to be a correlation is what we're going to answer. Well done!
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Frustrated with a particular MyStatLab/MyMathLab homework problem? No worries! I'm Professor Curtis, and I'm here to help.