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Peck, Olsen & Devore - Intro to Statistics 5/e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 7 / 100

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

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7/100 (7.0%)

  • Instructions

    Roxy Peck, Chris Olsen, and Jay Devore's 5th edition of Introduction to Statistics, published by Cengage Learning, uses real data and attention-grabbing examples to introduce students to the study of statistics and data analysis. Traditional in structure yet modern in approach, this text guides students through an intuition-based learning process that stresses interpretation and communication of statistical information. The WebAssign component for this text engages students with an interactive eBook and several other resources.

    Question 2 requires the student to calculate the frequency and relative frequency from a table of values, then construct, analyze, and infer information from the histogram to estimate a particular frequency.

    Questions 4, 5, and 6 show a variety of questions about probability and counting techniques.

    Question 7 is an Active Example from the textbook that walks the student through how to calculate a particular P-value for a normal distribution.

    Question 8 provides a link to the appendix tables available in the textbook that the student may use to calculate confidence intervals; however, the student may also use technology to calculate the value.

    Questions 9 and 10 ask the students to analyze different hypothesis tests.

    Question 11 asks the student to calculate the equation for the regression line and then compute values associated with the regression.

    Question 12 demonstrates a single-factor ANOVA F test.

    Question 13 is a Stats in Practice Question that demonstrates the use of videos displayed within a question, followed by multiple-choice and discussion questions in a unique two-part accordion-style type of display.

    Question 14 is a Test Bank question that highlights the ability to grade short answer style questions automatically using multiple choice.

    Question 15 is a Simulation Question utilizing the JMP Applet.

    Question 16 is an example of a Statistical Lab.

    Question 17 highlights Milestone 1, the first step in presenting and tracking Project Milestones for a statistical research project. 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 PODStat5 1.E.035. My Notes
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An article gave the following relative frequency distribution that summarized data on the type of violation for fines imposed on airlines by the Federal Aviation Administration.
Type of violation Relative frequency
Security 0.45
Maintenance 0.37
Flight operations 0.06
Hazardous materials 0.03
Other 0.09
(a) Use this information to construct a bar chart for type of violation.

Correct: Your answer is correct.


(b) Write a sentence or two commenting on the relative occurrence of the various types of violation.
By far the most frequently occurring violation categories were Correct: Your answer is correct. seenKey

security and maintenance

 . The least frequently occurring violation categories were Correct: Your answer is correct. seenKey

flight operations and hazardous materials

 .
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2. 4/11 points  |  Previous Answers PODStat5 3.E.026. My Notes
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Medicare's new medical plans offer a wide range of variations and choices for seniors when picking a drug plan. The monthly cost for a stand-alone drug plan varies from plan to plan and from state to state. The accompanying table gives the premium for the plan with the lowest cost for each state.
State Cost per Month (dollars)
Alabama 14.58
Alaska 7.69
Arizona 4.73
Arkansas 11.16
California 9.79
Colorado 6.01
Connecticut 9.65
Delaware 6.02
District of Columbia 1.87
Florida 15.66
Georgia 10.68
Hawaii 6.84
Idaho 9.52
Illinois 14.27
Indiana 1.87
Iowa 15.91
Kansas 13.62
Kentucky 10.47
Louisiana 5.62
Maine 5.12
Maryland 6.38
Massachusetts 7.73
Michigan 6.31
Minnesota 20.43
Mississippi 1.87
Missouri 1.87
Montana 9.64
Nebraska 1.87
Nevada 6.89
New Hampshire 8.84
New Jersey 7.12
New Mexico 10.30
New York 1.87
North Carolina 6.74
North Dakota 8.18
Ohio 12.35
Oklahoma 14.78
Oregon 16.14
Pennsylvania 8.62
Rhode Island 9.38
South Carolina 7.57
South Dakota 15.03
Tennessee 13.18
Texas 14.87
Utah 1.87
Vermont 8.85
Virginia 18.31
Washington 14.43
West Virginia 10.46
Wisconsin 7.63
Wyoming 19.67
(a) Use class intervals of $0 to <$3, $3 to <$6, $6 to <$9, etc., to create a relative frequency distribution for these data. (Round your answers for relative frequency to three decimal places.)
Class Interval Frequency Relative Frequency
$0 - <$3 Correct: Your answer is correct. seenKey

7

 		Correct: Your answer is correct. seenKey

0.137
$3 - <$6 3 0.059
$6 - <$9 Correct: Your answer is correct. seenKey

16

 		Correct: Your answer is correct. seenKey

0.314
$9 - <$12 Incorrect: Your answer is incorrect. seenKey

10
$12- <$15
$15 - <$18 4 0.078
$18 - <$21 3 0.059
TOTAL 51

(b) Construct a histogram.


Comment on its shape.
     Incorrect: Your answer is incorrect.

(c) Using the relative frequency distribution or the histogram, estimate the proportion of the states that have a minimum monthly cost of less than $12.00 a month. (Round your answer to one decimal place.)
Incorrect: Your answer is incorrect. seenKey

70.6

 %
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The standard deviation alone does not measure relative variation. For example, a standard deviation of $1 would be considered large if it is describing the variability from store to store in the price of an ice cube tray. On the other hand, a standard deviation of $1 would be considered small if it is describing store-to-store variability in the price of a particular brand of freezer. A quantity designed to give a relative measure of variability is the coefficient of variation. Denoted by CV, the coefficient of variation expresses the standard deviation as a percentage of the mean. It is defined by the formula CV = 100(s/ x ). Consider two samples. Sample 1 gives the actual weight (in ounces) of the contents of cans of pet food labeled as having a net weight of 8 oz. Sample 2 gives the actual weight (in pounds) of the contents of bags of dry pet food labeled as having a net weight of 50 lb. There are weights for the two samples.
Sample 1 8.8 7.8 7.2 8.9 7.2

8.8 8.6 7.4 7.4 7.2
Sample 2 50.7 52.7 51.6 51.4 52.2

47 50.4 50.3 48.7 48.2
(a) For each of the given samples, calculate the mean and the standard deviation. (Round your answers to five decimal places.)
For sample 1
Mean
Standard deviation

For sample 2
Mean
Standard deviation

(b) Compute the coefficient of variation for each sample. (Round your answers to two decimal places.)
CV1
CV2
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A deck of 52 cards is mixed well, and 5 cards are dealt.
(a) It can be shown that (disregarding the order in which the cards are dealt) there are 2,598,960 possible hands, of which only 1287 are hands consisting entirely of clubs.
What is the probability that a hand will consist entirely of clubs? (Give the answer to six decimal places.)


What is the probability that a hand will consist entirely of a single suit? (Give the answer to six decimal places.)


(b) It can be shown that exactly 63,206 hands contain only clubs and spades, with both suits represented.
What is the probability that a hand consists entirely of clubs and spades with both suits represented? (Give the answer to five decimal places.)


(c) Using the result of Part (b), what is the probability that a hand contains cards from exactly two suits? (Give the answer to five decimal places.)
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Jeanie is a bit forgetful, and if she doesn't make a "to do" list, the probability that she forgets something she is supposed to do is .5. Tomorrow she intends to run three errands, and she fails to write them on her list.
(a) What is the probability that Jeanie forgets all three errands?


What assumptions did you make to calculate this probability?
Events are .

(b) What is the probability that Jeanie remembers at least one of the three errands?


(c) What is the probability that Jeanie remembers the first errand but not the second or third?
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A store sells two different brands of dishwasher soap, and each brand comes in three different sizes: small (S), medium (M), and large (L). The proportions of the two brands and of the three sizes purchased are displayed as marginal totals in the table. Suppose that any event involving brand is independent of any event involving size. What is the probability of the event that a randomly selected purchaser buys the small size of Brand B1 (the event B1∩S)? What are the probabilities of the other brand-size combinations? (Fill up the table.)

Size
SML
BrandB1 0.70
B2 0.30

0.500.200.30
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Example 7.21 The probability P(z < -1.76) is found at the intersection of the -1.7 row and the .06 column of the z table (table of standard normal probabilities). The result is
P(z < -1.76) = .0392
as shown in the following figure:
In other words, in a long sequence of observations, roughly 3.9% of the observed z values will be smaller than -1.76. Similarly,
P(z .058) = entry in 0.5 row and .08 column of table of standard normal probabilities = .7190
as shown in the following figure:
Now consider P(z < -4.12). This probability does not appear in table of standard normal probabilities; there is no -4.1 row. However, it must be less than P(z < -3.89), the smallest z value in the table, because -4.12 is farther out in the lower tail of the z curve. Since P(z < -3.89) = .0000 (that is, zero to four decimal places), it follows that
P(z < -4.12) 0
Similarly,
P(z < 4.18) > P(z < 3.89) = 1.0000
from which we conclude that
P(z < 4.18) 1

What is the total area under the z curve?
    

Find the probability P(z > -1.76).
    


You may need to use the appropriate table in Appendix A to answer this question.
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In a survey of 505 potential jurors, one study found that 360 were regular watchers of at least one crime-scene forensics television series.
(a) Assuming that it is reasonable to regard this sample of 505 potential jurors as representative of potential jurors in the United States, use the given information to construct a 95% confidence interval for the true proportion of potential jurors who regularly watch at least one crime-scene investigation series. (Use Table 3 in Appendix A. Give the answer to three decimal places.)
( , )

(b) Would a 99% confidence interval be wider or narrower than the 95% confidence interval from Part (a)?
    


You may need to use the appropriate table in Appendix A to answer this question.
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For the following pairs, indicate which do not comply with the rules for setting up hypotheses, and explain why. (Select all that apply.)
(a)    H0: μ = 13, Ha: μ = 13

(b)    H0: p = 0.4, Ha: p > 0.7

(c)    H0: μ = 121, Ha: μ < 121

(d)    H0: μ = 121, Ha: μ = 122

(e)    H0: p̂ = 0.1, Ha: p̂ ≠ 0.1

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Breast feeding sometimes results in a temporary loss of bone mass as calcium is depleted in the mother's body to provide for milk production. An investigation gave the following data on total body bone mineral content (g) for a sample of mothers both during breast feeding (B) and in the postweaning period (P).
Subject 1 2 3 4 5 6 7 8 9 10
B 1926 2415 2201 2538 2368 2492 2655 1871 2500 2269
P 1957 2521 2375 2561 2518 2508 2764 2069 2574 2289
Do the data suggest that true average total body bone mineral content during postweaning exceeds that during breast feeding by more than 25 g? State and test the appropriate hypotheses using a significance level of 0.05. (Use a statistical computer package to calculate the P-value. Use μP − μB. Round your test statistic to two decimal places and the P-value to three decimal places.)
t =
df =
P =

Conclusion
    


You may need to use the appropriate table in Appendix A to answer this question.
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The accompanying data are x = advertising share and y = market share for a particular brand of cigarettes during 10 randomly selected years.
x 0.104 0.072 0.072 0.077 0.086 0.047 0.060 0.050 0.070 0.052
y 0.132 0.124 0.120 0.086 0.079 0.076 0.065 0.059 0.051 0.039
(a) Calculate the equation of the estimated regression line. (Round your answers to six decimal places.)
y =


Obtain the predicted market share when the advertising share is 0.09. (Round your answer to five decimal places.)


(b) Compute r2. (Round your answer to three decimal places.)


(c) Calculate a point estimate of σ. (Round your answer to four decimal places.)


On how many degrees of freedom is your estimate based?


You may need to use the appropriate table in Appendix A to answer this question.
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Give as much information as you can about the P-value of the single-factor ANOVA F test in each of the following situations. Use Table 6 in Appendix A.
(a) k = 5, n1 = n2 = n3 = n4 = n5 = 4, F = 5.05
P-value

(b) k = 5, n1 = n2 = n3 = 5, n4 = n5 = 4, F = 3.49
P-value

(c) k = 3, n1 = 4, n2 = 5, n3 = 6, F = 11.09
P-value

(d) k = 3, n1 = n2 = 4, n3 = 6, F = 14.11
P-value

(e) k = 4, n1 = n2 = 15, n3 = 12, n4 = 10, F = 1.87
P-value

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Stats in Practice

  • Part I - Multiple Choice Questions

    The video opens with: "Fewer young people are putting on sunscreen when they are having fun in the sun." They support this conclusion by citing the results of a Center for Disease (CDC) study, in which researchers estimated what value in both 2001 and 2011?
        
    In this CDC study, why is it correct to say that researchers "estimated" a particular population characteristic rather than say the researchers "calculated" that value?
        
    The video discusses a study conducted by University of Michigan researchers who found that "close community ties can reduce heart attack risk for those over 50." In this study, researchers probably collected a sample of individuals, and for each, measured numerical variables (such as age or weight) as well as categorical variables (such as gender or whether a person has had a heart attack). Which of the following is also a numerical variable that researchers may have measured in this study?
        
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A researcher is predicting that a treatment will increase scores. If this treatment is evaluated using a directional hypothesis test, then the critical region for the test would be the following.
    
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The population (in thousands) of 52 cities was collected and the graph and summary statistics of this data are given in the JMP Applet.

  • Cities' populations

    CITY POP
    ALBANY 846
    ALBUQUERQUE 486
    ATLANTA 2657
    ATLANTIC CITY 303
    BALTIMORE 2303
    BOSTON 2842
    BURLINGTON 127
    CHARLESTON 502
    CHARLOTTE 1091
    CHEYENNE 76
    CHICAGO 6199
    CINCINNATI 1438
    CLEVELAND 1851
    CITY POP
    DENVER 1645
    DES MOINES 385
    DETROIT 4362
    DUBUQUE 91
    GALVESTON-T.C. 211
    HARRISBURG 584
    HARTFORD 748
    HOUSTON 3228
    HUNTINGTON 323
    INDIANAPOLIS 1229
    JACKSON 396
    JACKSONVILLE 878
    LOS ANGELES 8505
    CITY POP
    LOUISVILLE 967
    MADISON 347
    MIAMI 1791
    MILWAUKEE 1389
    MINNEAPOLIS 2336
    MOBILE 438
    MONTGOMERY 297
    NASHVILLE 956
    NEW ORLEANS 1321
    NEW YORK 8529
    NORFOLK 1346
    OKLAHOMA CITY 975
    OMAHA 616
    CITY POP
    PHILADELPHIA 4866
    PHOENIX 1960
    PORTLAND 210
    PORTLAND 1168
    RALEIGH 665
    SALT LAKE CITY 1055
    SAN FRANCISCO 1590
    SEATTLE 1796
    SPOKANE 355
    ST. LOUIS 2458
    WASHINGTON 3646
    WICHITA 475
    WILMINGTON 559
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Statistical Lab

  • Background

    The National Institutes of Health conducts ongoing surveys of US adults called the Health Information National Trends Survey (hereafter abbreviated HINTS).
    From the National Institutes of Health: "The HINTS data collection program was created to monitor changes in the rapidly evolving field of health communication. Survey researchers are using the data to understand how adults 18 years and older use different communication channels, including the Internet, to obtain vital health information for themselves and their loved ones...."
    The most recent round of data collection occurred over the course of September 2013–November, 2013 in HINTS 4 Cycle 3. In this lab, you will be using a subset of the HINTS 4 Cycle 3 data to practice creating effective and informative graphical representations of data, which may include histograms and circle graphs.
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Milestone 1: Research Design

  • Question 1

    What is your research question?
    Your research question should be based on a topic that interests you and that you can reasonably obtain data for. Try to make your research question as specific as possible. Form a research question about a population that you will be able to sample. Some examples of research questions are: "Are students at my college able to taste the difference between regular coffee and decaffeinated coffee?", "Does the GPA, age, and number of credits needed for graduation for juniors at my university differ between transfer students and non-transfer students?", "Have the new water rates in my water district changed residents' water usage habits?", and "Do recent graduates from the business department at my university get larger starting salaries on average if they have participated in a summer internship?"

    This answer has not been graded yet.

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