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Probability and Statistics
Exam #1
Directions: Show all work in order to receive full credit.
Name: Solutions
1) A study is conducted on students taking a statistics class. Several variables are recorded in the survey. Identify
each variable as categorical or quantitative. (2 points each)
a) type of car the student owns : categorical
b) number of credit hours the taken during that semester : quantitative
c) the time the student waited in line at the bookstore to pay for his/her books : quantitative
d) Home state of the student: categorical
2) In the following graph, indicate whether it is symmetric, right skewed, or left skewed. Is the mean less than,
greater than, or equal to the median? (6 points)
Right skewed, mean>median
3) A histogram plots quantitative variables, while a bar chart plots categorical variables. (6 points)
4) For this problem use the following data: 1,8,9,10,12,14
a) Give the 5 point number summary.
(4 points)
Min=1, Q1=8, M=9.5, Q3=12, Max=14
b) Determine mathematically if there are any outliers. 1 is an outlier since 8-6=2 is the lower bound for
nonoutliers.
(4 points)
c) Draw an extended box plot of the data.
(2 points)
(graph)
Note: there should not be a line connected to the outlier.
d) Find the variance, and standard deviation.
(8 points)
Variance=20, standard deviation= 20
5)
a) Suppose you score 8 out of 10 on a quiz. The class average is 6 and the standard deviation is 2. What
percentage did better than you?
(5 points)
15.87 %
b) Suppose you don’t know your score on the quiz, but you know that 30.85% of the class did better than you.
What was your score?
(5 points)
7/10
6) Determine whether each of the following statements regarding a normal density curve is true or false.
a) it is symmetric (2 points) T
b) it has a peak centered above its mean (2 points) T
c) the quartiles lie 1 standard deviation below and above the mean (2 points) F
d) the spread of the curve is proportional to the standard deviation. (2 points) T
7) When creating a scatterplot, one should use the x-axis for the explanatory variable.
(2 points)
8) Select all descriptions that apply to the below scatterplot (6 points)
a) there is a positive association between height and volume.
b) There is a negative association between height and volume. This one
c) There is an outlier in the plot. And this one
9) A study found a correlation of r = -.61 between the gender of a worker and his or her income. Determine
whether each of the following conclusions regarding this correlation coefficient is true or false. (8 points)
a) women earn more than men on average F
b) women earn less than men on average F
c) an arithmetic mistake was made. Correlation must be positive. F
d) The measurement makes no sense; r can only be measured between two quantitative variables. T
10) A scatterplot of a variable Y versus a variable X produced the scatterplot shown below. The value of Y for all
values of X is exactly 1.0. (4 points)
What do we know about the correlation between X and Y?
a) It is +1 because the points lie perfectly on a line.
b) It is either +1 or -1, because the points lie perfectly on a line.
c) It is 0 because Y does not change as X increases. This one
d) None of the above
11) If we use a regression line to predict far outside of the range of data, we use the word extrapolate
(2 points)
12) In some example, suppose x = 5, y = 2, s = 6, s = 3 r = 4. Find the regression line.
(8 points)
Y(bar)=8x-38
13) Suppose we’re given r. What does r 2 mean?
(6 points)
The percentage of the data explained by the regression.
14) Correlation based on averages over many individuals is usually __________ than the correlation between the
same variables based on data for individuals.
a) lower
b) higher this one
c) cannot be decided
15) (6 points) see quiz #1 for similar question and answer.