Introduction Of Statistics

RM 150 Introduction to Statistics
Mr. Smith 30 April 2020
1
Final Exam
Use the following scenario to answer items 1-9.
Show all probabilities as a fraction, a decimal, and a percent.
Read ALL directions.
SHOW ALL WORK/PROCESS at every possible opportunity.
Round to TWO DECIMAL PLACES.
Scenario
Harris-Stowe State University has developed a mindfulness initiative, designed to alleviate stress
and improve performance on final exams. Research and evaluation randomly selected five
students from HSSU who reported their hours per week of mindfulness and their final exam
grade in their math class. The results are below.
1) Explain how the researchers accounted for potential bias in their study. [4 POINTS]
2) Provide an explanation for why “Scores” is the response variable. [5 POINTS]
3) Determine the mean of each of the sample groups (round to nearest tenth).
SHOW YOUR WORK. [8 POINTS; 4 POINTS EACH]
Hours ( ): __________
Scores ( ): __________
4) Using the other two measures of central tendency, explain whether or not (a) Hours and
(b) Scores are normally distributed. [6 POINTS; 3 POINTS EACH]
a)
b)
RM 150 Introduction to Statistics
Mr. Smith 30 April 2020
2
5) Create a scatterplot that reflects the data in the table. [5 POINTS]
6) State your observations from the scatterplot. What can you say about the relationship
between Hours and Scores? [5 POINTS]
7) Verify that the standard deviation of Hours is 2.28. [10 POINTS]
n x x – x (x – x)
2
1
2
3
4
5
[WORK SPACE]
Sum of Squares (SS): ________
s: __________
RM 150 Introduction to Statistics
Mr. Smith 30 April 2020
3
8) The correlation coefficient of the relationship between Hours and Scores is r = 0.96.
VERIFY that this is correct by calculating the r value, using the table below. Note that mean
and standard deviation information is below. [10 POINTS]
Write the verified correlation coefficient for the data.
9) The equation for the least squares regression line is as follows:
ŷ = 54.11 + 4.42x
a) What does the 4.42 mean in the context of the scenario? [4 POINTS]
b) What does the 54.11 mean in the context of the scenario? [4 POINTS]
c) If a student meditates 4 hours per week, what is there predicted math exam score?
[4 POINTS]
RM 150 Introduction to Statistics
Mr. Smith 30 April 2020
4
Use the following scenario to respond to items 10-13. Show all steps.
The following data represent the number of different communication activities (e.g., cell phone,
text messaging, e-mail, Internet, and so on) used by a random sample of teenagers over the past
24 hours.
10) What is the probability that a participant is male or uses no communication activities?
[5 POINTS]
11) What is the probability that a participant is female and uses 5 or more activities?
[5 POINTS]
12) What is the probability that a male participant uses 1-2 communication activities?
[5 POINTS]
13) What is the probability that a participant who uses 3-4 communication activities is female?
[5 POINTS]
Use the following scenario to respond to items 14-16. Show all steps.
You are invited to play a spinner game to the right. The
probabilities to land on each of the sections is as follows:
A: 25% B: 12.5% C: 12.5% D: 50%
The amount you win for landing on each section is listed. It costs
$1.00 to play each time.
14) What is the probability of landing on either A or D?
[5 POINTS]
15) What is the probability of landing on anything other than C? [5 POINTS]
16) What is the expected value for this game? [5 POINTS]
D
$2.00
A
$3.00
B
$5.00
C
-$10.00
RM 150 Introduction to Statistics
Mr. Smith 30 April 2020
5