Chapter 1
7. An education researcher randomly selects 38 schools from one school district and interviews all the teachers at
each of the 38 schools. Identify the type of sampling used in this example.
cluster
Round your answers to the nearest hundredth.
1. The employees in one department had to provide a report giving total mileage for the year for any work
related travel. Their mileages are shown below:
639 622 344 648 354 348 360 598 479 482
a) Find the mean
b) Find the sample standard deviation
c) Find the 5 number summary
d) Find the IQR
e) Calculate the outlier boundaries.
f) Are there any outliers for this dataset?
g) Draw a boxplot for this data
h) Is the distribution skewed or symmetric?
a. 487.4
b. 130.49
c. min=344, Q1=354, med=480.5, Q3=622, max=648
d. 268
e. lower fence = -48, upper fence = 1024
f. no outliers
1. For each statement below, identify which variable would be the predictor and which will be the response
variable.
a. A scientist is looking at the impact that the amount of sleep has on how tired you are.
b. A professor examines grades on the test to see if they are impacted by the amount of time spent on
homework.
A. Predictor: amt. of sleep. Response: how tired you are
B. Predictor: time on HW. Response: grade on test
Employees of a small company were asked about the transportation to work. Of the 20 employees, 3 walk to
work, 5 use public transportation, and the remaining employees drive their own car.
a. What is the sample space?
b. Create a probability model for this.
c. What is the probability that an employee selected at random drives to work?
d. What is the probability that an employee does not walk to work?
a. {walk, public, drive}
b. A | Walk |Public | Drive
P(A)| 0.15 | 0.25 |0.6
c. 0.60
d. 0.25 + 0.6 = 0.85
Suppose Joseph is about to take a multiple choice statistics test. There are four answer choices so if he guesses,
the probability of getting the question correct is 1/4 or 0.25. If there are 8 questions on the quiz and he
randomly guesses on every question, what is the probability of
a. Getting exactly 6 correct?
b. Getting exactly 0 correct?
a. Binompdf (8, 0.25, 6) = 0.0038
b. Binompdf (8, 0.25, 0) = 0.1001
8. At a college there are 120 freshmen, 90 sophomores, 110 juniors, and 80 seniors. A school administrator
randomly selects 12 of the freshmen, 9 of the sophomores, 11 of the juniors, and 8 of the seniors (taking 10% of
each level). She then interviews all the students selected. Identify the type of sampling used in this example.
Stratified
2. The number of cars passing through a bank drive-thru during each 15 minute period was recorded. The
results are shown below:
27 29 27 30 30 27 32 29 14 37 33
26 33 27 22 17 21 29 29 31 29 33
a) Find the mean
b) Find the sample standard deviation
c) Find the 5 number summary
d) Find the IQR
e) Calculate the outlier boundaries
f) Are there any outliers for this dataset?
g) Draw the boxplot
h) Is the distribution skewed or symmetric?
2. a. 27.82
b. 5.36
c. min=14, Q1=27, med=29, Q3=31, max=37
d. 4
e. lower fence = 21, upper fence = 37
f. two outliers, 14 and 17
5. Is your grade on the first unit test a good predictor of how well you will do in the STAT 1401 class? The
accompanying table lists the grades on the first test and the final average for students in a recent STAT 1401
class. Calculate the Pearson Correlation Coefficient.
Test 1 90 72 51 85 88 93 95 78 100 89
Final Avg 88 81 65 88 91 92 96 82 96 91
0.642
There are 5 red, 11 yellow, and 4 green balls in an bag.
a. Suppose you are going to draw out one ball and look at it. What is the sample space for this?
b. In drawing one ball, what is the probability that you will get a red ball?
c. In drawing one ball, what is the probability that you will get a yellow ball?
d. In drawing one ball, what is the probability that you will not get a green ball?
e. In drawing one ball, what is the probability that you will not get a yellow ball?
a. S = {R, Y, G}
b. 0.25
c. 0.55
d. 0.8
e. 0.45
A news article reported that 80% of college students change their major during their college career. Assume
that 20 students are randomly selected.
a. What is the probability that exactly 15 of those students changed their major?
b. What is the probability that exactly 10 of those students changed their major?
a. Binompdf (20, 0.8, 15) = 0.1746
b. Binompdf (20, 0.8, 10) = 0.002
9. Before premiering a blockbuster movie at a theater, test screenings are done beforehand. Each theater
premiering the movie is supposed to interview every 20th person as they leave the theater when the movie is
over. Identify the type of sampling used in this example.
systematic
4. The weight of 9 defensive linemen were 300 300 295 255 298 298 300 310 300
a. Give the Five Number Summary
b. Give the IQR
c. Give the outlier boundaries
d. Are there any outliers? If so, list them.
4. a. Defensive linemen: min = 255, Q1 = 296.5, med = 300, Q3= 300, max = 310
b. 3.5
c. lower boundary= 291.25 upper boundary = 305.25
d. yes, 255 and 310
11. Problem 5.42. Do beavers benefit beetles? Researchers laid out 23 circular plots, each 4 meters in diameter, in an area where
beavers were cutting down cottonwood trees. In each plot, they counted the number of stumps from trees cut by beavers and the
number of clusters of beetle larvae. Ecologists think that the new sprouts from stumps are more tender than other cottonwood
growth, so that beetles prefer them. If so, more stumps should produce more beetle larvae. Here are the data:
Stumps 2 2 1 3 3 4 3 1 2 5 1 3 2 1 2 2 1 1 4 1 2 1 4
Larvae 10 30 12 24 36 40 43 11 27 56 18 40 25 8 21 14 16 6 54 9 13 14 50
Assume the conditions are met and the line is a good fit.
a. Give the regression equation
b. Give the slope
c. Interpret the slope
d. Find the predicted value of larvae for 6 stumps.
e. Find the residual for 5 stumps. (hint: find the actual y value from the table above then calculate the predicted value
11.
a. Y-hat = -1.29 + 11.89x
b. 11.89 larvae/stump
c. As the number of stumps increase by 1, the number of larvae found will increase by 11.89
d. 70.05 larvae
e. -2.16 larvae
A quality control manager at Bugs Modem Sales uses test equipment to detect defective computer modems.
Thousands of modems are produced each day. A sample of 3 different modems is to be randomly selected from
a group that is reported to have a 13% defective rate. What is the probability that
a. All three are defective?
b. At least 1 selected modem is defective?
a. (.13)^3 = 0.0022
b. 1 – (.87)^3 = 0.3415
It is reported that 4% of American teens and adults have a food allergy. Assume we take a sample of 12
American teens and adults. Calculate the probability for the following:
a. What is the probability that exactly 3 of them have a food allergy?
b. What is the probability that exactly 8 of them have a food allergy?
a. Binompdf (12, 0.04, 3) = 0.0098
b. Binompdf (12, 0.04, 8) = 2.755 x 10-9
What variable type?
14. political party affiliation
Qualitative, Nominal
6. The average number of days absent per student per year at a local high school is 17 days with a standard deviation of
4 days. Find the z score for a student absent 6 days
6. - 2.75
7. A scientist collects data to predict the wheat yield (in bushels per acre) based on rainfall (in inches). The results
are recorded in the table below.
Rainfall in inches: 11.5 7.6 11.3 19.2 8.1 11.3 15.1 12.5
Wheat Yield: 62 26.5 52.5 81 40.5 42 73.2 55.1
Find the following:
a) correlation coefficient,
b) the regression equation
c) the slope.
d) interpret the slope
a) r = 0.926
b) 𝑦̂ = 0.39 + 4.45x or 𝑤ℎ𝑒𝑎𝑡 𝑦𝑖𝑒𝑙𝑑̂ = 0.39 + 4.45(𝑟𝑎𝑖𝑛𝑓𝑎𝑙𝑙)
c) slope = 4.45 bushels/inch
d) As rainfall increases by 1 inch, wheat yield increases by 4.45 bushels per acre
A 12-sided die can be made from a geometric solid called a dodecahedron. Assume that a fair dodecahedron is
rolled.
a. What is the sample space?
b. Find P(result less than 5)
a. S={1,2,3,4,5,6,7,8,9,10,11,12}
b. 0.3333
A local hospital is considering the purchase of a helicopter to transport critical patients. Let X be the random
variable representing the number of patients needing critical transport in a month based on data from a hospital
with a similar size and demographic.
X 0 1 2 3 4 5 6
P(X)0.15 0.2 0.34 0.19 0.06 0.05 0.01
a. What is the probability that 6 patients will need to be transported for critical care?
b. What is the probability that either 1 or 2 patients will need to be transported for critical care?
c. What is the probability that at least one patient will need to be transported for critical care?
d. What is the probability that no more than 3 patients will need to be transported for critical care?
e. What is the mean of the probability distribution?
f. What is the standard deviation of the probability distribution?
a. 0.01
b. 0.54
c. 0.85
d. 0.88
e. 2
f. 1.36
What Variable type?
Number of Siblings
Quantitative, discrete
7. The mean test score on the Chapter 5 mathematics test was 52 with a standard deviation of 14. Find the z score for a
test score of 95?
7. 3.07
6. A study was conducted to see if the average time spent in the lab each week affected course grade for computer
students. The results are recorded in the table below.
Number of Hours spent in lab: 10 12 15 9 7 14 15 16 11
Grade (points): 95 75 77 52 89 88 80 45 58
Find the following:
a. correlation coefficient.
b. Describe the association
6.
a. r = -0.218
b. The association is negative and weak
You flip a fair coin four times. List the possible outcomes. (there will be 16 of them)
HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT
THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT