A group of students takes a 10 point quiz. You have the scores for each student...

A group of students takes a 10 point quiz. You have the scores for each student and decide to calculate the correlation between (a) the number of correct answers on the quiz with (b) the number of incorrect answers on the quiz.

A. What would r equal? If you’re stuck, think about this a bit. If you’re really stuck, it may help to make a scatterplot based 10 students getting various scores on the quiz. _________________ (1 point)

B. How did you arrive at your conclusion? (1 point)

Solutions

Expert Solution

a) We are computing the correlation coefficient between the number of correct answers on the quiz and the number of incorrect answers on the quiz. As the number of correct answers increases in the quiz , and as the number of questions is constant, the number of incorrect answers would always decrease in the quiz. Therefore there is a negative correlation between the number of correct answers and the number of incorrect answers in the quiz. Therefore the correlation coefficient r here would be given as: r = -1

b) The reason for r = -1 is that for a unit increase in correct number of answers, there would be a unit decrease in the number of incorrect answers and also for a unit decrease in correct number of answers, there would be a unit increase in the number of incorrect answers. This shows a perfect negative correlation between the two variables. Therefore r = -1 is the required correlation coefficient as it represents the perfect negative correlation between 2 variables.

orchestra answered 1 year ago

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