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
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
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
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
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