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Statistics, section 2, Fall 2019
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Peck & Short,Statistics:Learning from Data(AP) 2/e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 14 / 75

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

Last Saved : n/a Saving... ()

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Question

Points

1	2	3	4	5	6	7	8	9	10	11	12
2/3	1/20	3/3	8/8	–/5	–/4	–/11	–/6	–/10	–/3	–/1	–/1

Total

14/75 (18.7%)

Instructions

Statistics: Learning From Data (AP^® Edition), 2nd edition, 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. 2/3 points | Previous Answers PeckStat2HS 2.E.016.MI.S. My Notes

A report on Americans' opinions about long-term investments included data from a poll of 1,010 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	0.23
Gold	0.18
Savings	0.16
Bonds	0.08
Other	0.03

A button hyperlink to the SALT program that reads: Use SALT.

(a)

Use this information to construct a bar chart for the response data.

A bar chart has 6 categories along the horizontal axis. The horizontal axis is labeled "Best Long-Term Investment." The vertical axis is labeled "Relative Frequency" and ranges from 0.00 to 0.32. The bars are centered over their respective category labels, and moving from left to right their heights are as follows.
Real Estate: about 0.32
Stocks & Mutual Funds: about 0.18
Gold: about 0.23
Savings: about 0.08
Bonds: about 0.16
Other: about 0.03

(b)

Comment on how people responded to the question posed.

% of respondents answered that the best long-term investments were real estate and stocks and mutual funds, and the remaining

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

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2. 1/20 points | Previous Answers PeckStat2HS 2.E.026. My Notes

Question Part

Points

Submissions Used

1/1

–/1

0/1

–/1

1/100

0/100

1/100

0/100

Total

1/20

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	36.3	Montana	39.2	Rhode Island	39.2
Alaska	32.8	Indiana	36.8	Nebraska	35.7	South Carolina	37.7
Arizona	35.1	Iowa	38.0	Nevada	35.4	South Dakota	36.7
Arkansas	37.2	Kansas	35.9	New Hampshire	40.4	Tennessee	37.8
California	34.7	Kentucky	37.6	New Jersey	38.7	Texas	33.1
Colorado	35.7	Louisiana	35.3	New Mexico	35.5	Utah	28.9
Connecticut	39.5	Maine	42.3	New York	38.0	Vermont	41.1
Delaware	38.5	Maryland	37.6	North Carolina	36.9	Virginia	36.8
DC	35.2	Massachusetts	39.2	North Dakota	36.2	Washington	37.1
Florida	40.2	Michigan	38.6	Ohio	38.4	West Virginia	40.6
Georgia	34.8	Minnesota	37.4	Oklahoma	35.9	Wisconsin	38.3
Hawaii	37.5	Mississippi	35.0	Oregon	38.2	Wyoming	35.8
Idaho	34.0	Missouri	37.5	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\|9 =	28.9 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 2.8. 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 , with .

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3. 3/3 points | Previous Answers PeckStat2HS 2.E.055. My Notes

4. 8/8 points | Previous Answers PeckStat2HS 3.E.014.S. My Notes

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)

Calculate the mean and standard deviation for this data set (in millions of dollars). (Round your answers to four decimal places.)

mean $

million standard deviation $

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 $

million standard deviation $

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

and the standard deviation

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

, because outliers

a significant impact on those measures.

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5. –/5 points PeckStat2HS 3.E.036.S. My Notes

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	106,169	IN	268,231	NC	48,168	RI	30
AR	73,592	KS	30,035	ND	55,217	SC	26,793
AZ	23,703	KY	188,129	NE	65,838	SD	15,356
CA	241	LA	80,147	NH	3,181	TN	56,419
CO	38,301	MA	10,855	NJ	2,446	TX	365,521
CT	1,121	MD	25,131	NM	17,749	UT	21,158
DE	2,254	ME	887	NV	7,441	VA	38,792
FL	89,079	MI	194,404	NY	17,811	VT	16
GA	80,963	MN	24,380	OH	282,000	WA	2,873
IA	76,858	MO	141,444	OK	74,439	WI	62,448
ID	21	MS	77,500	OR	14,018	WV	86,215
IL	135,880	MT	16,230	PA	252,092	WY	40,685

Use these data to calculate the values (in tons) in the five-number summary. (Hint: See Example 3.13.)

smallest observation tons lower quartile tons median tons upper quartile tons largest observation tons

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6. –/4 points PeckStat2HS 4.E.032.S. My Notes

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	2.10
Delta	86	0.74
Envoy Air	74	1.57
Express Jet	78	1.03
Frontier	73	3.89
Hawaiian	88	0.87
JetBlue	76	1.15
SkyWest	80	0.82
Southwest	80	0.51
Spirit	68	Not reported
United	78	2.73
Virgin America	81	Not reported

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 = +

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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7. –/11 points PeckStat2HS 4.E.042.MI.S. My Notes

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)
3–5	4.0	543.3
6–8	7.0	585.0
9–11	10.0	668.3
12–15	13.5	701.1
16–18	17.0	728.6

(a)

With x = representative age and y = median distance walked in 6 minutes, construct a scatterplot.

A scatterplot has 5 points.

The horizontal axis is labeled "x" and ranges from 500 to 750.

The vertical axis is labeled "y" and ranges from 0 to 20.

The points are plotted from left to right in an upward, diagonal direction starting from the lower left corner of the diagram.

The points have little scatter and are between the approximate horizontal axis values of 540 and 730 and between the approximate vertical axis values of 4 and 17.

A scatterplot has 5 points.

The horizontal axis is labeled "x" and ranges from 0 to 20.

The vertical axis is labeled "y" and ranges from 500 to 750.

The points are plotted from left to right in a downward, diagonal direction starting from the upper left corner of the diagram.

The points have little scatter and are between the approximate horizontal axis values of 4 and 17 and between the approximate vertical axis values of 540 and 730.

Does the pattern in the scatterplot look linear?

The scatterplot shows a curved pattern. The scatterplot shows no pattern at all. The scatterplot shows a linear pattern.

(b)

Find the equation of the least-squares regression line. (Round your values to three decimal places.)

ŷ = +

(c)

Calculate the five residuals. (Round your answers to three decimal places.)

Representative Age (x)	Residual
4.0
7.0
10.0
13.5
17.0

Construct a residual plot.

A residual plot has 5 points.

The horizontal axis is labeled "x" and ranges from 0 to 18.

The vertical axis is labeled "Residual" and ranges from approximately −36 to 36.

There is a horizontal line that spans the graph at 0 on the vertical axis.

There are 3 points above the line and 2 points below the line.

Moving from left to right, the points begin above the horizontal line, move up and to the right, then down and to the right crossing the horizontal line, then move back up and to the right, cross the horizontal line again, and end at the upper right corner.

The points vary between approximately −28 and 18 on the vertical axis. The maximum residual is at x = 17 while the minimum is at x = 10.

Are there any unusual features in the plot? (Hint: See Examples 4.6 and 4.7.)

The residual plot reflects the sharp increase in the median distance walked between the representative ages of 10 and 13.5. There are no unusual features in the plot. The residual plot reflects the sharp decrease in the median distance walked between the representative ages of 10 and 13.5. The residual plot reflects the sharp decrease in the median distance walked between the representative ages of 7 and 10. The residual plot reflects the sharp increase in the median distance walked between the representative ages of 7 and 10.

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8. –/6 points PeckStat2HS 5.E.014. My Notes

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.)

(b)

Are the outcomes in the sample space equally likely?

Yes No

(c)

What is the probability that both selected students are statistics majors?

(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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9. –/10 points PeckStat2HS 5.E.034.MI. My Notes

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, 46% purchase the extended warranty for the dryer, and 58% 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
Not W
Total			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

(ii)

the probability that a randomly selected customer purchases an extended warranty for neither the washer nor the dryer

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10. –/3 points PeckStat2HS 6.E.009. My Notes

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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11. –/1 points PeckStat2HS 7.AP.008. My Notes

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?

(A) The doctors can perform a hypothesis test to determine if there is evidence for the claim that the mean number of clinic visits for patients who eat an apple every day is less than the mean number of clinic visits for patients who eat less than one apple per week. (B) The doctors can estimate mean number of clinic visits over the 2-year period for both patient groups. (C) The doctors can perform a hypothesis test to determine the mean number of apples eaten by patients. (D) Both A and B are true. (E) No conclusion can be drawn from this study since there was no random assignment to treatments.

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12. –/1 points PeckStat2HS FT5.8.014. My Notes

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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