Question

Which one of the following is a true statement about the correlation coefficient r?

The unit of measure for r is the same as the unit of measure for the response variable y. Values of r range from -∞ to +∞.

If the sign of r is negative, then increases in one variable tend to be associated with decreases in the other variable.

The designations of which is the explanatory variable and which is the response variable cannot be interchanged when calculating r.

r is resistant to outliers.

6. The standard deviation of the sampling distribution of x̄ for samples of size 15, is smaller than the standard deviation of the population. True False

Answer 1

Please kindly note that when there is negative correlation then increase in one variable tend to result in decrease of other variable. And negative correlation coefficient is denoted by negative sign.

Hence If the sign of r is negative, then increases in one variable tend to be associated with decreases in the other variable is the true statement about correlation coefficient r.

6. Suppose population standard deviation = and we have given n= 15

Then we know that the standard deviation of x bar is

Hence when n= 15 then the standard deviation of x bar become which is smaller than

Hence the standard deviation of the sampling distribution of x̄ for samples of size 15, is smaller than the standard deviation of the population is TRUE statement.

Hope this will help you. :)