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

검증된 단계별 안내

Step 1: Count the number of pairs of data (n) in the dataset provided. Each pair consists of one value from Sprint and one value from Verizon. In the table, there are 8 pairs of data.

Step 2: Refer to Table 2-11 to find the critical value of r for n = 8. From the table, the critical value of r for n = 8 is 0.707.

Step 3: Compare the given linear correlation coefficient r = 0.866 with the critical value of r = 0.707. If the absolute value of r is greater than the critical value, there is significant evidence of a linear correlation.

Step 4: Since r = 0.866 is greater than the critical value of 0.707, conclude that there is a significant linear correlation between the Sprint and Verizon data speeds.

Step 5: Interpret the result: The significant linear correlation suggests that as one variable (e.g., Sprint data speed) increases, the other variable (e.g., Verizon data speed) tends to increase as well, indicating a positive relationship.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Linear Correlation Coefficient (r)

The linear correlation coefficient, denoted as r, quantifies the strength and direction of a linear relationship between two variables. Its value ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation. In this context, an r value of 0.866 suggests a strong positive correlation between the data sets being analyzed.

Critical Values of r

Critical values of r are threshold values that determine the significance of the correlation coefficient in hypothesis testing. These values depend on the sample size and the chosen significance level (commonly 0.05). By comparing the calculated r value to the critical values, one can conclude whether the observed correlation is statistically significant or likely due to random chance.

Statistical Significance

Statistical significance indicates whether the results observed in a study are likely to be genuine or if they could have occurred by random chance. In the context of correlation, if the calculated r exceeds the critical value for a given sample size, the correlation is considered statistically significant, implying that there is a reliable relationship between the variables being studied.

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