Midterm - Introductory Statistics - F24 - B.docx

Introductory Statistics

1. Date: Monday 4/11/2024 Instructor Name: Dr. Amal Mohamed
Name: _________________________ ID: ______________________
Instructions:
1-The Academic Integrity code applies to this test.
2-You have 75 minutes to finish the exam!
PART Question Possible points Score
I MCQs 20
II Question 1 14
Question 2 12
Question 3 8
Question 4 5
Question 5 12
Total
Worth 15%
50
BONUS
0.5%
Question 6 9

2. Part I: Multiple Choice Questions (MCQs)
1.The summaries of data, which may be tabular, graphical, or numerical, are referred to as
A.inferential statistics
B. descriptive statistics
C.statistical inference
D.report generation
2.A Statistics professor asked students in a class about their ages. On the basis of this information,
the professor states that the average age of all the students in the university is 24 years. This is
an example of
A.a census
B.descriptive statistics
C.an experiment
D.statistical inference
3.A frequency distribution is a tabular summary of data showing the
A.fraction of items in several classes
B.percentage of items in several classes
C.relative percentage of items in several classes
D.number of items in several classes
4.Fifteen percent of the students in a school of Business Administration are majoring in
Economics, 20% in Finance, 35% in Management, and 30% in Accounting. The graphical
device(s) which can be used to present these data are
A.a line graph
B.only a bar graph
C.only a pie chart
D.both a bar graph and a pie chart
5.A histogram is said to be skewed to the left if it has a
A. longer tail to the right
B. shorter tail to the right
C. shorter tail to the left
D. longer tail to the left
6.Which of the following statements about the mean is not always correct?
a.The sum of the deviations from the mean is zero
b.Half of the observations are on either side of the mean
c.The mean is a measure of the (center) of a distribution
d.The value of the mean times the number of the observations equals the sum of all of the
observations
7.The percent frequency of a class is computed by 
a. multiplying the relative frequency by 10 
b. dividing the relative frequency by 100 
c. multiplying the relative frequency by 100 
d. adding 100 to the relative frequency
8.In constructing a frequency distribution, the approximate class width is computed as 
a. (largest data value - smallest data value)/number of classes
b. (largest data value - smallest data value)/sample size 
c. (smallest data value - largest data value)/sample size 
d. largest data value/number of classes

3. 9.The interquartile range 
 a. is a measure of location 
 b. is a measure of variability 
 c. is always equal to the median  
 d. is always equal to the mode 
10.If the mode is to the left of the median and the mean is to the right of the median, the distribution
is:
a. skewed to the right.
b. skewed to the left.
c. symmetric.
d. None of the above.
11.The number of customers that enter a store during one day is an example of
a. nominal variable
b. qualitative variable
c. continuous variable
d. discrete variable.
12.The following scatter diagram shows that the relationship between X and Y is
a. Linear and Positive
b. Linear and Negative
c. No relation
d. Not linear
13.For the information shown in the box plot below, what is the range and what is the interquartile
range?
a. Range=15, IQR=10
b. Range=14, IQR=10
c. Range ¿14,IQR=9
d. Range=5.5, IQR=4.5
14.In constructing a frequency distribution, as the number of classes are decreased, the class width
a. Decreases
b. remains unchanged
c. Increases
d. can increase or decrease depending on the data values
15.The mean monthly rent for a sample of studio apartments in one city is $1220 with a standard
deviation of $210. The monthly rents for eight more studio apartments in the city are listed. Using
the sample statistics above, determine which of the data values are unusual. Are any of the data
values very unusual? Explain. (Assume the data set has a bell-shaped distribution.)
$1073, $1577, $1682, $1892, $821, $1703, $1346, $695
a.$1682, $1892, $1703, $695 are unusual because they are more than 2 standard deviations from
the mean. $1892 is very unusual because it is more than 3 standard deviations from the mean.

4. b.$1577, $1682, $1892, $821, $1703, $695 are unusual because they are more than 1 standard
deviation from the mean. $1682, $1892, $1703, $695 are very unusual because they are more
than 2 standard deviations from the mean.
c.$1892 is unusual because it is more than 3 standard deviations from the mean. There are no
values that are very unusual because no value is more than 4 standard deviations from the mean.
d.$1682, $1892, $821, $1703, $695 are unusual because they are more than 2 standard deviations
from the mean. $1892 and $695 are very unusual because they are more than 3 standard
deviations from the mean.
16.A regression analysis between weight (y in pounds) and height (x in inches) resulted in the
following least squares line: ^y
= 120 + 5x. This implies that if the height is increased by 1 inch,
the weight, on average, is expected to:
a.increase by 1 pound
b.decrease by 1 pound
c.increase by 5 pounds
d.increase by 24 pounds
17.A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following
least squares line: ^y
= 75 +6x.This implies that if advertising is $800, then the predicted amount
of sales (in dollars) is:
a.$4875
b.$123,000
c.$487,500
d.$12,300
18.a coefficient of correlation r = - 0.92 indicates a ….
a. weak association
b. strong association
c. strong negative association
d. strong positive association
19.Which of the following pairs of statements cannot be true?
a. y = 3 – 5x and r = 0.20
b. y = 6 – 8x and r = - 0.40
20.The median of the following data set: 5, 8, -1, 2, 7, 6, and -4 is:
a. 2
b. 9
c. 5
d. 4.5

5. Part II: Free Response Questions
Q1. [14 pts.] Short-Answered Questions
A.Indicate which of the following variables are quantitative and which are qualitative:
a. Colors of cars
b. Number of persons in a family
c. Marital status
d. Time needed to complete a task
e. Number of typing errors in a document
B.Identify the level of measurement for the following:
a. A military title
b. Heat measured in degrees centigrade
c. Number of goals scored by football player during a season
d. Field position of a football player (goalkeeper, forward, midfield, etc)
e. City traffic during the rush hour (light, medium, heavy)
C.We wish to measure the body temperature of all the children in a family:
a. Classify as either a census or a sample and explain your answer.
b. What is the data collecting method?
d. What is the variable of interest?
e. What is the type of this variable?

6. Q2. [15 pts.] (A.) State whether the following statements are TRUE or FALSE. If TRUE, give a brief (1
sentence) reason to explain why; if FALSE, change (or add) a single word in the statement so that it
becomes true.
(a) The mean is resistant against the effect of outliers
(b) Half of the observations always lie on one side of the mean, while half lie on the other side.
(c) In a Normal distribution, the mean is equal to the median.
(B.)Give an example of a data set with 4 observations, in which the standard deviation is equal to 0.
If this is not possible, then give a brief (1 sentence) reason.
(C.) The following graph shows the distribution of a group of students according to the time(in minutes)
they take to solve a Statistics midterm exam
1The name of the variable in this study is ________________
2The type of the variable is ¿
¿ and its level of measurement is __________________
3This graph is called a ¿
¿ and its shape is ____________________
4The total number of students in this study is equal to ___________________
5The percentage of students who solved the midterm exam in less than 50 minutes is equal to ___

7. Q3. [8 pts.]Are good grades associated with family togetherness?
A random sample was done of 142 students in the USA, asking them for their GPA and how many meals
per week their family ate together. The correlation was 0.43; the students’ GPA had a mean of 2.75 and a
standard deviation of 0.64. The number of meals/week they spent with their family had a mean of 3.78
and a standard deviation of 2.2. [Hint: Use r=
S
xy
S
xS
y
to get b=
S
xy
S
x
2]
(a) Suppose you want to predict GPA as a function of how many meals/week a family eats together. Give
the regression model to make this prediction.
(b) What is the meaning of the intercept in this context?
(c) The difference between the GPA’s of two good friends is 1.00; can you expect the difference in the
number of meals per week their family ate together?
(d) Is the number of meals a family eats together a good predictor of GPA? Explain your answer.

8. Q4. [5 pts.]The hourly wages of a sample of eight individuals is given below.
Individual Hourly Wage (dollars)
A27
B25
C20
D10
E12
F14
G17
H19
For the above sample, determine the following measures:
a.The mean and interpret your result.
b.The standard deviation.
c.The 25th percentile and interpret your result.

9. Q5. A. [4 pts.] A sample of 5 observations has a variance of 27. If we know that ∑x
2
=288 :
a.Compute the sample mean.
b.What is the effect of multiplying all observations by 10 on the mean and the variance?
B. [8 pts.] Indicate whether each of the following statements is true (T) or false (F) and explain your
answer:
(a) When X is a binary variable coded as 1=Yes and 0=No, then the sum of the data is equal to the
number of people who said No.
(b) For each of the last 10 years, we recorded whether a company has made profit (1), loss ( -1 ), or
broke even (0), then the sum of the absolute value of the data is the same as the number of years in
which the company has made profit.
(c) Approximately 68% of all observations in any data set fall within one standard deviation of the
mean.
(d) A dataset has a mean of 5 and a variance of 10 . If we multiply each observation in the dataset by
3 then add 5, the new dataset will have a mean of 20.

10. BONUS (1%)
Across
3.- A data point that is FAR AWAY from all
other data points
4.- The MIDDLE number in an ORDERED data
set.
8.- Differences in data. How the data VARIES.
9.- The MOST COMMON data point in a data
set.
   
Down
1.- The difference between the upper quartile &
the lower quartile. The middle 50% of data
2.- Questions with answers involving a mass
(group) of numerical data
5.- The AVERAGE of a data set.
6.- Numbers that are used to gather information.
7.- The DIFFERENCE between the greatest &
least data points.