Question

A statistician wants to determine the relationship between typing speed, in words per minute, and the time, in minutes, it takes to type one page of a specific book. Twenty-five trials are completed and the correlation coefficient between typing speed and time is determined to be -0.622. Therefore, slower typing speed was related to greater time. How is the correlation affected if the units for time are changed from minutes to seconds?

Select one:
a. The correlation and time measurement would change proportionally to one another.
b. The correlation would stay the same because the change in units for time would have no effect on it.
c. The correlation would increase because changing the units for time would result in an increase in time values.
d. It is impossible to determine the amount of change experienced by the correlation.
e. The correlation would decrease because only the units for one of the variables changed.

Answer 1

B

Explanation:

The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. It is calculated using a formula that takes into account the values of the two variables and their relationship to each other. This formula is not affected by changes in the units of measurement of either variable. Therefore, changing the units of time from minutes to seconds in this scenario would not affect the value of the correlation coefficient, so it would remain the same.

Option A, "The correlation and time measurement would change proportionally to one another," is incorrect because the correlation coefficient is not affected by changes in the units of measurement of either variable.

Option C, "The correlation would increase because changing the units for time would result in an increase in time values," is also incorrect because the correlation coefficient is not affected by changes in the actual values of the variables, only by the strength and direction of the relationship between them.

Option D, "It is impossible to determine the amount of change experienced by the correlation," is incorrect because, as explained above, the correlation coefficient is not affected by changes in the units of measurement of either variable.

Option E, "The correlation would decrease because only the units for one of the variables changed," is also incorrect because, as explained above, the correlation coefficient is not affected by changes in the units of measurement of either variable.