Testing for Rank Correlation
In Exercises 7–12, use the ...

Question

Testing for Rank Correlation

In Exercises 7–12, use the rank correlation coefficient to test for a correlation between the two variables. Use a significance level of α = 0.05.

Colombian Coffee The following table lists quality rankings and costs (dollars) for a pound of different brands of Colombian coffee (based on data from Consumer Reports). Lower values of the quality rankings correspond to better coffee. Do the more expensive brands appear to have better quality?

Accepted Answer

All right, hello, everyone. So this question says, the following table lists battery life in hours of continuous usage and prices in US dollars for different smartphone models. Use the rank correlation coefficient or Spearman's row, to test the hypothesis of a correlation between battery life and price. Use alpha equals 0.05. What conclusion can you draw? All right, so first and foremost, what you want to do is rank not only the battery life, but the price of each smartphone. With one being the smallest number. So when starting off with the ranking of the battery life. The corresponding rank for each is as follows in order from smartphone A through H. So, The corresponding ranks for each smartphone are 63. 85. 14. 7 and 2. And it just so happens that the same ranking applies. For the price as well. So going from smartphone A through H, the rankings are also 6,38514, 7, and 2. And so what this means is that not only. Will the differences between each rank be zero, but the square of the differences will also be zero, which means that the sum of all of the differences squared will also be zero. The reason why I bring that up is because of the formula for Spearman's rank correlation coefficient or row. Row, if you recall, is equal to 1, subtracted by 6 multiplied by the sum of all differences squared. And divided by N multiplied by N2 subtracted by 1. Plugging in the information found before, you would see that 1 or that row is equal to 1 subtracted by 6 multiplied by 0. Divided by 8, multiplied by 8 squares subtracted by 1. And so because the second term of the expression will ultimately equal 0, row is equal to 1 in this case. Which now brings us to the hypothesis test. Now the null hypothesis H not would simply state that row is equal to zero, meaning there is no correlation between. Between battery life and price. Therefore, the alternative hypothesis. Would simply state. That row is not equal to 0, meaning that there is some correlation. So now this brings us to the critical value. Now the critical value. For Spearman's coefficient. At alpha equals 0.05 for a two-tailed test with 8 degrees of freedom, because that's the sample size, is positive or negative, 0.738. And now, we've arrived at our final answer, right? Because our calculated value for row, which is equal to 1, is greater than the critical value of 0.738, we can reject the null hypothesis. And so the correct answer reads as follows. There is a significant positive correlation between battery life and price. And there you have it. So with that being said, thank you so very much for watching and I hope you found this helpful.

��app

Key Concepts

Rank Correlation Coefficient

Significance Level (α)

Hypothesis Testing

Watch next