Suggested Exercises 2
Math 150
Directions: In this document you will find fifteen questions I have written for your practice. I would recommend you attempt as many of these as possible to make sure you’re familiar with not only the concepts presented in each section but also the types of questions that are associated with these topics. If you have any questions send me an email, ask during class, or see me during office hours.
Question 1) Consider the following data that shows the miles per gallon a car gets while driv-ing at a particular speed.
MPH MPG 20 21 30 24 35 27 40 28 50 34 60 27 70 25 80 20
(a) What is the explanatory variable? What is the response variable? (b) Construct a scatterplot for this data.
(c) Calculate the correlation coefficient. Does this value make sense? Why or why not?
Question 2) For each of the following situations identify the explanatory and response variable. Then decide if you think the association will most likely be positive or negative.
(a) Suppose we want to study the relationship between salary at a large business firm and years of experience working in the business field.
Question 3) Suppose I am interested in studying the relationship between height and weight for adult males. I take a large sample of adult males and measure their height in inches and their weight in pounds. Then I construct the following LSR wherey represents the weight andx represents the height. Note: All our subjects were between 62 inches and 74 inches tall.
ˆ
y= 10x−450 r=.85
(a) Give the value of the slope of this LSR. Then interpret this value in context of the situa-tion.
(b) Give the value of the intercept of this LSR. Then interpret this value in context of the situation. (c) Give the value of the coefficient of determination. Then write a sentence interpreting this value. (d) Predict the weight of an adult male who is 52 inches tall. Would you trust this prediction? Why or why not?
For Questions 4 and 5 use the following data that shows a random sample of 7 individuals, their FICO Credit Scores and the Interest Rate they were offered by a credit card company.
Note: Credit Scores are measured on a scale from 300 to 800 and are used to determine insurance, mortage, and credit card rates. A higher credit score represents a better credit history.
Credit Score Interest Rate (in %)
525 26.5
545 19.0
595 18.0
640 12.2
675 8.6
705 6.7
750 5.2
Question 4) Construct a scatterplot for this data. What variable is the explanatory variable? What variable is the response variable? What is the correlation coefficient? Is there enough evidence for an association?
Question 5) Construct the LSR for this data. Interpret the slope and intercept. What is the coefficient of determination? If someone with a credit score of 680 was offered an interest rate of 8.3% would this be a good offer?
For Questions 6 and 7 use the following data about wind chill.
The wind chill factor depends on wind speed and air temperature. We collect the following data on 7 days where the air temperature was 15◦F.
Wind Speed (mph) Wind Chill (◦F)
5 12
10 -3
15 -11
20 -17
25 -22
30 -25
35 -27
Question 6) Construct a scatterplot for this data. Give the correlation coefficient. Is there enough evidence for an association?
Question 7) Construct the LSR for this data. Give the coefficient of determination. Then build a residual plot for this data. Is the LSR an appropriate model here? Why or why not?
Question 8) Suppose you are interested in studying the relationship between ages of students at a local university and choice of major. You gather records from the school and get the following data.
18-21 22-25 25+
STEM 323 118 127
Social Sciences 518 205 113 Arts+Humanities 457 313 95
Business 116 84 78
(a) What was the size of your sample?
(b) If you were to randomly select someone out of your sample what is the chance that person is between 22 and 24 years old and is majoring in arts and humanities?
(c) Construct the conditional distribution based on age. Comment on the preferences of students in the 18-21 age group.
(d) Construct the conditional distribution based on major. Which major has the highest percentage of older (25+ years old) students?
Question 9) Consider the following probability experiment. You roll two six sided dice. You record the maximum value rolled between the two dice. For example, if you roll a 3 and a 5 you would record a 5. If you roll a 2 and a 2 you would record a 2.
(a) Write down a probability model for this probability experiment.
(b) What is the chance you record an even number in this probability experiment? (c) What is the chance you record a number greater than 4?
(d) What is the chance you record a number that is at least 1?
Question 10) The random variable below shows the number of cats owned by randomly selected US adults.
# of cats Probability
0 .61
1 .22
2 .09
3 .04
4 .02
5 .015
6 .005
(a) Confirm that this is a probability model.
(b) Draw a probability histogram for this random variable.
(c) Calculate the mean and standard deviation of this random variable. Interpret the mean in context of this situation.
(d) What is the chance that a randomly chosen American adult owns more than 4 cats? (e) What is the chance that a randomly chosen American adult owns at least 1 cat?
Question 11) Consider the following table that shows the results of a sample of 100 El Camino students where they were asked what their field of study currently was and their favorite math course.
Algebra Statistics Calculus
STEM 11 3 21
Social Sciences 5 15 5 Arts/Humanities 15 20 5
(a) What is the probability that a randomly chosen student from this sample chose Algebra as their favorite math course?
(b) What is the probability that a randomly chosen student from this sample indicated that Arts/Humanities was their field of study?
(c) What is the probability that a randomly chosen student from this sample indiciated that STEM was their field of study and that Calculus was their favorite math course?
(d) What is the probability that a randomly chosen student from this sample indcated that Social Sciences was their field of study or that statistics was their favorite math course?
(e) What is the probability that a randomly chosen student from this sample said statistics was their favorite math course given that this student was studying the social sciences?
(f) Are the events studying STEM and having Algebra as your favorite course indpendent? Show a calculation to support your asnwer.
Question 12) For each of the following password rules, find the total number of passwords pos-sible.
(a) Suppose a password consists of the 10 digits scrambled into some order (no repeats). So a typical password would be 1543897062.
(b) Suppose a pssowrd consists of 4 digits (without repeats) and then 3 letters (repeats allowed). So a typical password be 4325aba.
(c) Which type of password would be harder to guess randomly?
Question 13) Suppose that you have a bag that contains a bunch of different colored marbles. There are 5 red marbles, 6 blue marbles, 5 green marbles, and 4 white marbles. Suppose you pull out 4 marbles randomly from the bag.
(a) Calculate the probability that you pull out all blue marbles.
Question 14) Tom Brady’s highest completion rate for passes was 69%. Suppose that each pass he throws is independent. Suppose that you watch him throw 15 passes.
(a) Calculate the probability that he completes exactly 10 of the 15 passes. (b) Calculate the probability that he misses exactly 3 of the 15 passes. (c) Calculate the probability that he misses more than 1 of the 15 passes.
Question 15) Suppose you roll a fair six-sided die 100 times. You record the number of 6’s you roll. (a) Explain why this can be treated as a binomial random variable.
(b) Confirm that it is appropriate to use the normal approximation to the binomial distribution in this situation.
(c) Calculate the mean and standard deviation of this binomial random variable. (d) Approximate the chance that you roll more than 25 6’s on your 100 rolls. (e) If you did roll more than 25 6’s on 100 rolls what might you conclude?
Suggested Textbook Exercises from Moore ”The Basic Practice of Statistics”:
Chapter 4: 4.14 - 4.23, 4.24 - 4.30, 4.38 - 4.40 Chapter 5: 5.20 - 5.29, 5.30 - 5.31, 5.35 - 5.36, 5.40 Chapter 6: 6.8 - 6.15, 6.18 - 6.23, 6.25, 6.28, 6.30 Chapter 12: 12.22 - 12.31, 12.33 - 12.38, 12.42 - 12.45
Chapter 13: 13.17 - 13.26, 13.28 - 13.30, 13.36, 13.39, 13.40, 13.48 Chapter 14: 14.13 - 14.21, 14.22 - 14.26, 14.33 - 14.35
