STATS CHAPTER 4
A perfect straight line sloping downward would produce a correlation coefficient equal to:
-1.0
Which of the following are measures of the linear relationship between two variables?
Both covariance and correlation
A scatter diagram reveals a strong positive linear relationship between oil and gasoline prices. Which of the following numerical techniques will not give us more detailed information about this relationship?
Coefficient of variation.
Graphical and numerical techniques, such as histograms and least squares lines provide identical information.
False
If the coefficient of correlation r = 0, then there can be no relationship whatsoever between the dependent variable y and the independent variable x.
False
If the mean, median, and mode are all equal, the histogram must be symmetric and bell shaped.
False
When the standard deviation is expressed as a percentage of the mean, the result is the coefficient of correlation.
False
Which of the following statements about the median is not true?
It is more affected by extreme values than the mean.
Which of the following summary measures is sensitive to extreme values?
Mean
Which measure of central location can be used for both interval and nominal variables?
Mean Median Mode
The precision provided by the numerical techniques (mean, median, and standard deviation) provides more useful information than graphical techniques (histograms and box plots) alone.
True
The value of the mean times the number of observations equals the sum of the observations.
True
When the distribution is symmetric and unimodal, mean = median = mode.
True
Generally speaking, if two variables are unrelated (as one increases, the other shows no pattern), the covariance will be:
a positive or negative number close to zero.
If the correlation coefficient r = 1.00, then all the observations must fall exactly on:
a straight line with a positive slope.
The median of an ordered data set with 30 items would be the average of the 15th and the 16th observations
True
Which of the following statistics is a measure of central location?
The mean The mode The median
Which of the following characteristics does a histogram help you identify?
The shape of distribution. The amount of spread in a distribution. The approximate center of a distribution.
If the coefficient of correlation r = 0, then there can be no linear relationship between the dependent variable y and the independent variable x.
True
In a bell shaped distribution, there is no difference in the values of the mean, median, and mode.
True
In a histogram, the proportion of the total area which must be to the right of the mean is exactly 0.50 if the distribution is symmetric and unimodal.
True
Statisticians typically apply graphical techniques as a first step in a data analysis because we first need to know the shape of the distribution.
True
The coefficient of correlation and the least squares line both describe the relationship between two interval variables.
True
The mean is affected by extreme values but the median is not.
True
In a histogram, the proportion of the total area which must be to the left of the median is:
exactly 0.50.
The strength of the linear relationship between two interval variables can be measured by the:
coefficient of correlation.
In a histogram, the proportion of the total area which must be to the right of the mean is:
exactly 0.50 if the distribution is symmetric and unimodal.
Which of the following is a property of r, the coefficient of correlation?
r always lies between 0 and 1. r has no units. If you switch the values of X and Y, the sign of r changes.
In a perfectly symmetric bell shaped "normal" distribution:
the median equals the mode. the mean equals the median. the mean equals the mode.