Airport Data Speeds Listed below are the cellular data speeds ...

Question

Airport Data Speeds Listed below are the cellular data speeds (Mbps) from Sprint and Verizon measured at nine different airports (based on data from CNN). What would the presence of a correlation suggest about Sprint and Verizon?

Table comparing cellular data speeds (Mbps) for Sprint and Verizon at nine airports.

Accepted Answer

Hello, everyone. Let's take a look at this question together. The table listed below shows the average gasoline prices in US dollars per gallon at 9 different locations for two major fuel brands, Brand A and Brand B. What would the presence of a correlation suggest about the relationship between these two brands' pricing strategies across different locations? And here we have our table containing the 9 different locations, as well as the prices for both Brand A and Brand B. Is it answer choice A, there is a weak correlation, meaning the prices are mostly independent. Answer choice B, there is a moderate negative correlation, meaning as one brand's price increases, the other decreases. Answer choice C. There is a strong positive correlation, meaning the prices move together in the same direction, or answer choice D, there is no correlation between the two brands' prices. So in order to check the presence of correlation about the relationship between the two brands' pricing strategies across the different locations, we must first calculate the correlation coefficient R, which can be done. Using the formula for the correlation coefficient r, and so we will create the following table to calculate the formula for the correlation coefficient. Starting with the value for X bar, which is calculated using the sum of the X values divided by 9, and plugging in the data from our table, we get the value of 3.3278 as the value for X bar. Then we calculate. The value for Y bar, which is the sum of the Y values divided by 9, which plugging in the values from our table gives us 3.3944 as the value for Y bar. And so we calculate the sum of in parentheses X minus X bar multiplied by in parentheses Y minus Y bar using those values, which gives us 0.17883, as well. As the sum of X minus X squared, which is 0.205562, and lastly the sum of Y minus Y squared, which is 0.15722, and substituting all of the values that we have calculated into our correlation coefficient formula gives us 0.99475, which rounded is 0.9948, as The value for the correlation coefficient R and using the correlation coefficient value of R equals 0.9948, we note that the correlation coefficient is very close to 1, which indicates a very strong positive correlation between gasoline prices of brand A and Brand B. So this suggests that as the price of Brand A increases, the price of Brand B. Also increases in a nearly linear fashion, and the strong correlation implies that the two brands might be following similar pricing strategies, possibly due to market competition or shared external factors like supply costs. So the presence of a correlation about the relationship between the prices of Brand B and Brand A, we know there is a very strong Positive correlation between the gasoline prices of both brands as the correlation coefficient of 0.9948 is very close to one. And looking at our answer choices, we can identify that answer choice C is the correct answer, as there is a strong positive correlation between the two brands' prices, meaning the prices move together in the same direction. So answer choice C is correct, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

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