Use Table 2-11 to find the critical values of r. Based on a co...

Question

Use Table 2-11 to find the critical values of r. Based on a comparison of the linear correlation coefficient r and the critical values, what do you conclude about a linear correlation?

Using the data from Exercise 6 “Airport Data Speeds,” the linear correlation coefficient is r = 0.866

Table comparing data values for Sprint and Verizon, showing numerical statistics across various categories.

Table displaying critical values of r based on the number of data pairs, with values ranging from 0.576 to 0.950.

Accepted Answer

Hello, everyone, let's take a look at this question together. The table one listed below shows the average gasoline prices in US dollars per gallon at 9 different locations for two major fuel brands, brands A and B. The linear correlation coefficient is R equals 0.995. Use table 2 to find the critical values of R. Based on a comparison of the linear correlation coefficient R and the critical values, what do you conclude about a linear correlation? Is it answer choice A? There is no significant correlation between the variables. Answer choice B, there is a significant correlation, and it is strong. Answer choice C, there is a significant correlation and it is weak, or answer choice D, the correlation is inconclusive based on the given data. So using the provided data to determine if there is a linear correlation, we must first identify the critical value of R for our sample size, which in this case the sample size is 9, as there are 9 locations, so the sample size of 9. Yields a critical value of 0.666. And then using our R critical value of 0.666, we must compare the given correlation coefficient, which is R equals 0.995. And given both the R critical value and the R value, we know that correlation exists if the computed linear correlation coefficient. lies in the left or right tail region bounded by the table value for that tail. So if that linear correlation coefficient is in the left or right tail region, there is sufficient evidence to support the claim of a linear correlation. However, there is no correlation if the computed linear correlation coefficient R lies between the two critical values. If the linear correlation coefficient R, which is 0.995, lies in the left or right tail region bounded by the table value for that tail, there is in fact sufficient evidence to support the claim of linear correlation. However, if that coefficient is between the two critical values of 0.666, then there is not sufficient evidence. To support the claim of a linear correlation and using this diagram to determine if there is correlation or no correlation, we have our two correlation regions and our no correlation region between the two critical values. Well, given that our correlation coefficient is 0.995, we know that this value exists beyond the critical values. And therefore, it falls within the correlation region. So looking at our answer choices, we can identify that answer choice B is the correct answer, as there is in fact significant correlation, since the linear correlation coefficient R exists well beyond the critical values. So, answer choice B is correct, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

Use Table 2-11 to find the critical values of r. Based on a comparison of the linear correlation coefficient r and the critical values, what do you conclude about a linear correlation?
Using the data from Exercise 6 “Airport Data Speeds,” the linear correlation coefficient is r = 0.866

Key Concepts

Linear Correlation Coefficient (r)

Critical Values of r

Statistical Significance

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