Question

mrs. rawls create her scatterplot using the following data. the same data that was used in the previous question. mr. latterner created a scatterplot with different data and had a correlation coefficient of -0.40. choose all the following statements that are true. mr. latterners data has a positive slope while mrs. rawls data has a negative slope. both data can be categorized as strong data. both data have a negative slope. mrs. rawls data will be more condensed than mr. latterners data. there is not enough information given to answer this problem. mrs. rawls data is considered strong while mr. latterners data is considered weak. minutes % remaining 90 41 65 63 22 88 30 82 45 79 99 38 15 93 75 50 111 35 80 47

Explanation:

Step1: Recall correlation - coefficient concept

The correlation coefficient \(r\) measures the strength and direction of a linear relationship. A positive \(r\) indicates a positive - slope relationship, and a negative \(r\) indicates a negative - slope relationship. The closer \(|r|\) is to 1, the stronger the relationship.

Step2: Analyze Mr. Latterner's data

Mr. Latterner has a correlation coefficient of \(- 0.40\). Since \(r=-0.40\), the data has a negative slope. And since \(| - 0.40|\) is not close to 1 (a common rule - of - thumb for strong correlation is \(|r|\geq0.7\)), it is not strong data.

Step3: Analyze Mrs. Rawls' data

No information about Mrs. Rawls' correlation coefficient is given, so we cannot say if her data is strong or weak.

Step4: Evaluate each statement

• “Mr. Latterner's data has a positive slope while Mrs. Rawls' data has a negative slope.” - False, Mr. Latterner's data has a negative slope.
• “Both data can be categorized as strong data.” - False, Mr. Latterner's data is not strong.
• “Both data have a negative slope.” - We don't know about Mrs. Rawls' data slope.
• “Mrs. Rawls' data will be more condensed than Mr. Latterner's data.” - No information to support this.
• “There is not enough information given to answer this problem.” - True as we lack key information about Mrs. Rawls' data like the correlation coefficient.
• “Mrs. Rawls' data is considered strong while Mr. Latterner's data is considered weak.” - We don't know if Mrs. Rawls' data is strong.

Answer:

There is not enough information given to answer this problem.