Question

ch 4 a statistics professor warns her class that her second midterm is always harder than the first. she tells her class that students always score 10 points worse on the second midterm compared to their score on the first midterm. this means that the correlation between students scores on the first and second exam is -1 cant tell without seeing the data. +1 question 7 1 pts ch 4 researchers collect data on 5,134 american adults younger than 60. they measure the reaction times (in seconds) of each subject to a stimulus on a computer screen and how many years later the subject died. the researchers are interested in whether reaction time can predict time to death (in years). when you make a scatterplot, the explanatory variable on the x axis can be either reaction time or time to death. is the reaction time. is the time to death.

Explanation:

• For the first question: The relationship \(y=x - 10\) (where \(y\) is the second - midterm score and \(x\) is the first - midterm score) is a perfect linear relationship. The formula for the correlation coefficient \(r=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})}{\sqrt{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}\sum_{i = 1}^{n}(y_{i}-\bar{y})^{2}}}\). If \(y=ax + b\) (\(a>0\)), then \(r = 1\). Here \(a = 1\) (since \(y=x-10\)), so the correlation is \(+1\).
• For the second question: In a scatter - plot, the explanatory variable (also known as the independent variable) is plotted on the \(x\) - axis. The researchers want to see if reaction time (\(x\)) can predict time to death (\(y\)). By the definition of an explanatory variable in a prediction context (where \(x\) is used to predict \(y\)), the explanatory variable on the \(x\) - axis is the reaction time.

Answer:

• First question: \(+1\)
• Second question: is the reaction time.