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Peck, Stats: Learning from Data (AP) 2/e Update (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 24 / 75

Due : Sunday, January 27, 2030 23:30 EST

Last Saved : n/a Saving...  ()

Question
Points
1 2 3 4 5 6 7 8 9 10 11 12
3/3 2/20 3/3 0/1 7/8 –/5 –/4 3/11 1/6 5/10 –/3 –/1
Total
24/75 (32.0%)
  • Instructions

    Statistics: Learning From Data (AP® Edition), 2nd edition Update, by Roxy Peck and Tom Short, published by Cengage Learning, addresses common problems faced by students and instructors with an innovative approach to elementary statistics. The organization by Learning Objective, focus on real-data examples, and adherence to the Guidelines for Assessment and Instruction in Statistics Education (GAISE), help students learn to think like statisticians. The AP edition includes exam tips throughout the text along with sections designated to address common errors on the AP exam.

    Question 1 includes an example of a table, bar graphs, and the fill-in-the-blank method which is often used for short-answer style questions.

    Question 2 demonstrates how one way stem-and-leaf displays can be graded.

    Question 3 utilizes a series of multiple-choice questions to guide students through the interpretation and analysis of a real world figure.

    Question 4 demonstrates how one way numerical grading is achieved as well as short-answer fill-in-the-blank grading methods. Students can use SALT to answer this question.

    Question 5 demonstrates the grading of a five-number summary problem. Students can use SALT to answer this question.

    Question 6 shows how problems involving least-squares regression lines are handled in this textbook. Students can use SALT to answer this question.

    Question 7 has examples of scatterplots, the grading of a least-squares regression line, residuals, and residual plots. Students can use SALT to answer this question.

    Question 8 demonstrates the grading of a sample space presented as an unordered list.

    Question 9 is an example of a problem involving a hypothetical 1,000 table.

    Question 10 allows lists of numbers to be graded.

    Question 11 is an AP practice question.

    Question 12 is a Fast Track to a Five question. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

    The answer key and solutions will display after the first submission for demonstration purposes. Instructors can configure these to display after the due date or after a specified number of submissions.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1. 3/3 points  |  Previous Answers PeckStat2HSU 1.3.016.MI.S. My Notes
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Points
Submissions Used
1 2 3
1/1 1/1 1/1
1/100 1/100 1/100
Total
3/3
 
A report on Americans' opinions about long-term investments included data from a poll of 1,030 adults. The responses to the question "What do you think is the best long-term investment?" are summarized in the given relative frequency distribution.
Response Relative
Frequency
Real Estate 0.32
Stocks & Mutual Funds 0.21
Gold 0.19
Savings 0.17
Bonds 0.06
Other 0.05
A button hyperlink to the SALT program that reads: Use SALT.
(a)
Use this information to construct a bar chart for the response data.

(b)
Comment on how people responded to the question posed.
Correct: Your answer is correct. seenKey

53

% of respondents answered that the best long-term investments were real estate and stocks and mutual funds, and the remaining Correct: Your answer is correct. seenKey

47

% of respondents believed that gold, savings, bonds, and other were the best long-term investment.

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2. 2/20 points  |  Previous Answers PeckStat2HSU 1.4.026. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
/1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 1/1 1/1
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2/20
 
A certain newspaper gave the following data on median age for each of the 50 U.S. states and the District of Columbia (DC) in a particular year.
State Median
Age
State Median
Age
State Median
Age
State Median
Age
Alabama 37.5 Illinois 36.1 Montana 39.0 Rhode Island 39.1
Alaska 32.9 Indiana 36.7 Nebraska 35.7 South Carolina 37.7
Arizona 35.0 Iowa 38.2 Nevada 35.6 South Dakota 36.9
Arkansas 37.2 Kansas 35.7 New Hampshire 40.3 Tennessee 37.8
California 34.9 Kentucky 37.8 New Jersey 38.7 Texas 33.0
Colorado 35.6 Louisiana 35.3 New Mexico 35.5 Utah 28.7
Connecticut 39.6 Maine 42.1 New York 38.0 Vermont 41.3
Delaware 38.5 Maryland 37.8 North Carolina 36.7 Virginia 36.9
DC 35.0 Massachusetts 39.0 North Dakota 36.4 Washington 37.2
Florida 40.2 Michigan 38.6 Ohio 38.4 West Virginia 40.4
Georgia 34.8 Minnesota 37.2 Oklahoma 35.9 Wisconsin 38.3
Hawaii 37.6 Mississippi 35.2 Oregon 38.2 Wyoming 35.7
Idaho 34.0 Missouri 37.7 Pennsylvania 39.7
Construct a stem-and-leaf display using stems
28, 29,   , 42.
(Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)
stems: ones
leaves: tenths
28|7 =28.7 years
Stem Leaves
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
Comment on shape, center, and variability of the data distribution. Are there any unusual values in the data set that stand out? (Hint: See Example 1.9. Round your center to the nearest integer.)
The distribution of median ages is centered at approximately years, with values ranging from a minimum of years to a maximum of years. The distribution is Correct: Your answer is correct. seenKey

approximately symmetric

, with Correct: Your answer is correct. seenKey

one possible outlier

.
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3. 3/3 points  |  Previous Answers PeckStat2HSU 1.5.046. My Notes
Question Part
Points
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1 2 3
1/1 1/1 1/1
1/100 2/100 1/100
Total
3/3
 
The following display is similar to one that appeared in USA TODAY. It is meant to be a bar graph of responses to the question shown in the display.
An infographic shows a bar chart made of images with the caption "If you were given $1,000, what would you do?" The bars are ordered from left to right by decreasing height and value as follows.
  • The bar labeled "Put it in general savings" is an image of a bank and has the value 48%.
  • The bar labeled "Pay off credit card debt" is an image of a credit card and has the value 27%.
  • The bar labeled "Put it in children's education fund" is an image of a graduation hat and diploma and has the value 12%.
  • The bar labeled "Use it for health care expenses" is an image of the Red Cross symbol and has the value 10%.
  • The bar labeled "Put it toward vacation" is an image of a beach and has the value 10%.
At the bottom is text that says "Source: Bank of America Consumer Purchasing and Savings Habits survey of 1,000 adults 18 and older. Margin of error ±4 percentage points."
(a)
Is response to the question a categorical or numerical variable?
     Correct: Your answer is correct.
(b)
Explain why a bar chart rather than a dotplot was used to display the response data.
     Correct: Your answer is correct.
(c)
There must have been an error made in constructing this display. How can you tell that it is not a correct representation of the response data?
     Correct: Your answer is correct.
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4. 0/1 points  |  Previous Answers PeckStat2HSU 11.AP.008. My Notes
Question Part
Points
Submissions Used
1
0/1
1/100
Total
0/1
 
The doctors at a local clinic would like to determine if "an apple a day" really does keep the doctor away. The doctors plan to examine the frequency of clinic visits for people who eat an apple a day and for people who eat less than one apple a week. They are going to conduct a study with 50 people in each group.
Fifty clinic patients who report that they routinely eat an apple a day and 50 clinic patients who report that they eat less than one apple a week will be identified. The doctors will examine the patients records to determine the number of clinic visits the patients have had over the past 2 years. They will then compare the mean number of clinic visits for the two groups.
Suppose that the two groups can be considered random samples that are representative of the corresponding populations. Which of the following are correct statements given the description of the study?
     Incorrect: Your answer is incorrect.


Solution or Explanation
(D). The doctors can either estimate the mean number of clinic visits for each of the two populations or test hypotheses about the difference in mean number of clinic visits for the two populations. Answer choice (C) is not viable because the number of apples eaten for each of the study participants is not known.
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5. 7/8 points  |  Previous Answers PeckStat2HSU 2.2.014.S. My Notes
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0/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1
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7/8
 
Consider the following data on the estimated cost (in millions of dollars) resulting from traffic congestion for different urban areas. The following are the data for the 13 largest U.S. urban areas.
Urban Area Total Cost
(millions of dollars)
New York 15
Los Angeles 14
Chicago 7
Washington, D.C. 5
Houston 5
Dallas, Fort Worth 4
Detroit 4
Miami 4
Phoenix 4
Philadelphia 4
San Francisco 3
Boston 3
Atlanta 3
A button hyperlink to the SALT program that reads: Use SALT.
(a)
Calculate the mean and standard deviation for this data set (in millions of dollars). (Round your answers to four decimal places.)
mean $ Incorrect: Your answer is incorrect. seenKey

5.7692

million
standard deviation $ Correct: Your answer is correct. seenKey

4.0240

million
(b)
Delete the observations for New York and Los Angeles and recalculate the mean and standard deviation (in millions of dollars). (Round your answers to four decimal places.)
mean $ Correct: Your answer is correct. seenKey

4.1818

million
standard deviation $ Correct: Your answer is correct. seenKey

1.1677

million
Compare this mean and standard deviation to the values calculated in part (a).
When New York and Los Angeles were excluded from the data set, the mean Correct: Your answer is correct. seenKey

decreased

and the standard deviation Correct: Your answer is correct. seenKey

decreased

.
What does this suggest about using the mean and standard deviation as measures of center and variability for a data set with outliers?
This suggests that using the mean and standard deviation as measures of center and variability for data sets with outliers present Correct: Your answer is correct. seenKey

can be risky

, because outliers Correct: Your answer is correct. seenKey

seem to have

a significant impact on those measures.
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6. /5 points PeckStat2HSU 2.4.036.S. My Notes
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/1 /1 /1 /1 /1
0/100 0/100 0/100 0/100 0/100
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/5
 
Suppose that the U.S. Environmental Protection Agency reported the following sulphur dioxide emissions (in tons) for the 48 states in the continental United States for a particular year.
State SO2
Emissions
State SO2
Emissions
State SO2
Emissions
State SO2
Emissions
AL 106,164 IN 268,226 NC 48,163 RI 25
AR 73,587 KS 30,030 ND 55,212 SC 26,788
AZ 23,698 KY 188,124 NE 65,833 SD 15,351
CA 236 LA 80,142 NH 3,176 TN 56,414
CO 38,296 MA 10,850 NJ 2,441 TX 365,516
CT 1,116 MD 25,126 NM 17,744 UT 21,153
DE 2,249 ME 882 NV 7,436 VA 38,787
FL 89,074 MI 194,399 NY 17,806 VT 11
GA 80,958 MN 24,375 OH 281,995 WA 2,868
IA 76,853 MO 141,439 OK 74,434 WI 62,443
ID 16 MS 77,495 OR 14,013 WV 86,210
IL 135,875 MT 16,225 PA 252,087 WY 40,680
A button hyperlink to the SALT program that reads: Use SALT.
Use these data to calculate the values (in tons) in the five-number summary. (Hint: See Example 2.13.)
smallest observation tons lower quartile tons median tons upper quartile tons largest observation tons
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7. /4 points PeckStat2HSU 3.4.047.S. My Notes
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Points
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1 2 3 4
/1 /1 /1 /1
0/100 0/100 0/100 0/100
Total
/4
 
A report on airline quality included the accompanying data on the on-time arrival percentage and the number of complaints files per 100,000 passengers for U.S. airlines.
Airline On-Time
Arrival Percentage
Complaints per
100,000 Passengers
Alaska 86 0.40
American 80 2.14
Delta 86 0.70
Envoy Air 74 1.57
Express Jet 78 1.03
Frontier 73 3.89
Hawaiian 88 0.87
JetBlue 76 1.19
SkyWest 80 0.86
Southwest 80 0.55
Spirit 67 Not reported
United 78 2.69
Virgin America 79 Not reported
A button hyperlink to the SALT program that reads: Use SALT.
The report did not include data on the number of complaints for two of the airlines. Use the given data from the other airlines to fit the least squares regression line. (Round your answers to four decimal places.)
ŷ =
x
Use the least squares regression line to predict the number of complaints per 100,000 passengers for Spirit and for Virgin America. (Round your answers to two decimal places.)
Spirit complaints per 100,000 Virgin America complaints per 100,000
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8. 3/11 points  |  Previous Answers PeckStat2HSU 3.5.057.MI.S. My Notes
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Points
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1 2 3 4 5 6 7 8 9 10 11
1/1 1/1 0/1 0/1 0/1 /1 /1 /1 /1 1/1 0/1
1/100 1/100 1/100 1/100 1/100 0/100 0/100 0/100 0/100 1/100 1/100
Total
3/11
 
Two hundred and eighty boys completed a test that measures the distance that the boy can walk on a flat, hard surface in 6 minutes. For each age group shown in the table, the median distance walked by the boys in that age group is given.
Age Group Representative
Age (Midpoint
of Age Group)
Median Six-Minute
Walk Distance
(meters)
35 4.0 543.3
68 7.0 585.0
911 10.0 666.3
1215 13.5 701.1
1618 17.0 728.6
A button hyperlink to the SALT program that reads: Use SALT.
(a)
With x = representative age and y = median distance walked in 6 minutes, construct a scatterplot.

Correct: Your answer is correct.
Does the pattern in the scatterplot look linear?
     Correct: Your answer is correct.
(b)
Find the equation of the least-squares regression line. (Round your values to three decimal places.)
ŷ = Incorrect: Your answer is incorrect. seenKey

491.824

Incorrect: Your answer is incorrect. seenKey

14.858

x
(c)
Calculate the five residuals. (Round your answers to three decimal places.)
Representative
Age (x)
Residual
4.0 Incorrect: Your answer is incorrect. seenKey

-7.956

7.0
10.0
13.5
17.0
Construct a residual plot.

Correct: Your answer is correct.
Are there any unusual features in the plot? (Hint: See Examples 3.11 and 3.12.)
     Incorrect: Your answer is incorrect.

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9. 1/6 points  |  Previous Answers PeckStat2HSU 5.2.014. My Notes
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Total
1/6
 
A college job placement center has requests from five students for employment interviews. Three of these students are math majors, and the other two students are statistics majors. Unfortunately, the interviewer has time to talk to only two of the students. These two will be randomly selected from among the five.
(a)
What is the sample space for the chance experiment of selecting two students at random? (Hint: You can think of the students as being labeled A, B, C, D, and E. One possible selection of two students is A and B. There are nine other possible selections to consider.) (Enter your answers in the form AB. Enter your answers as a comma-separated list.)
AB,A
Incorrect: Your answer is incorrect. webMathematica generated answer key
(b)
Are the outcomes in the sample space equally likely?
     Correct: Your answer is correct.
(c)
What is the probability that both selected students are statistics majors?
Incorrect: Your answer is incorrect. seenKey

0.1

(d)
What is the probability that both students are math majors?
(e)
What is the probability that at least one of the students selected is a statistics major?
(f)
What is the probability that the selected students have different majors?
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10. 5/10 points  |  Previous Answers PeckStat2HSU 5.3.034.MI. My Notes
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0/1 0/1 1/1 0/1 0/1 1/1 1/1 1/1 1/1 0/1
1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100
Total
5/10
 
An appliance manufacturer offers extended warranties on its washers and dryers. Based on past sales, the manufacturer reports that of customers buying both a washer and a dryer, 32% purchase the extended warranty for the washer, 49% purchase the extended warranty for the dryer, and 61% purchase at least one of the two extended warranties.
(a)
Use the given probability information to set up a hypothetical 1,000 table. (Let W be the event that the customer purchases an extended warranty for the washer. Let D be the event the customer purchases an extended warranty for the dryer.)
D Not D Total
W Incorrect: Your answer is incorrect. seenKey

200

Incorrect: Your answer is incorrect. seenKey

120

Correct: Your answer is correct. seenKey

320

Not W Incorrect: Your answer is incorrect. seenKey

290

Incorrect: Your answer is incorrect. seenKey

390

Correct: Your answer is correct. seenKey

680

Total Correct: Your answer is correct. seenKey

490

Correct: Your answer is correct. seenKey

510

1,000
(b)
Use the table from part (a) to find the following probabilities.
(i)
the probability that a randomly selected customer who buys a washer and a dryer purchases an extended warranty for both the washer and the dryer
Correct: Your answer is correct. seenKey

0.2

(ii)
the probability that a randomly selected customer purchases an extended warranty for neither the washer nor the dryer
Incorrect: Your answer is incorrect. seenKey

0.39



Solution or Explanation
(a)
When a customer buys both a washer and a dryer, let W be the event that the customer purchases an extended warranty for the washer, and let D be the event the customer purchases an extended warranty for the dryer.
D Not D Total
W 200 120 320
Not W 290 390 680
Total 490 510 1,000
(b)
We use the table from part (a) to find the following probabilities.
(i)
P(W D) = 
200
1,000
 = 0.2
(ii)
P(Wc Dc) = 
390
1,000
 = 0.39

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11. /3 points PeckStat2HSU 6.1.009. My Notes
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/1 /1 /1
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/3
 
Two six-sided dice, one red and one white, will be rolled. List the possible values for each of the following random variables. (Enter your answers as comma-separated lists.)
(a)
x = sum of the two numbers showing
(b)
y = difference between the number on the red die and the number on the white die (red white)
(c)
w = largest number showing
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/1
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/1
 
A large company wants to estimate the proportion of employees who would prefer a pay increase to an increase in retirement benefits using a 95% confidence interval. What sample size should be used in order to achieve a margin of error of 0.04 or smaller?
    
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