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Think and Answer requires you to answer two questions

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Think and Answer requires you to answer two questions. For each question, do not simply provide an answer; make sure you explain how you arrived at that answer. Even if your reasoning is wrong, you will still be credited for participation.

Each weekly Think and Answer post(s) is worth 2% of your final grade.

 

Week 1 Think and Answer

 

What is Wrong with These Statements?

1. The air temperature was 33° F in the night and 66° F in the day. So in the day it was twice as warm as in the night.

2. The United Nations Organization declared that the world’s six-billionth inhabitant was born on October 12, 1999 in Bosnia.

True or False?

3. When we are selecting the class width, we may, for more convenience, round it off to the nearest whole number.

4. If you add 1 to each score in a data set, the mean for this set will also increase by 1.

HomeWork Week 1

Ch.1

Sec 1-1: 

 Statistical Literacy and Critical Thinking

1. Online Medical Info USA Today posted this question on its website: “How often do you seek medical information online?” Of 1072 Internet users who chose to respond, 38% of them responded with “frequently.” What term is used to describe this type of survey in which the people surveyed consist of those who decided to respond? What is wrong with this type of sampling method?
2. Reported Versus Measured In a survey of 1046 adults conducted by Bradley Corporation, subjects were asked how often they wash their hands when using a public restroom, and 70% of the respondents said “always.”
   1. Identify the sample and the population.
   2. Why would better results be obtained by observing the hand washing instead of asking about it?

Sampling Method. In Exercises 9–12, determine whether the sampling method appears to be sound or is flawed.

9.  Nuclear Power Plants In a survey of 1368 subjects, the following question was posted on the USA Today website: “In your view, are nuclear plants safe?” The survey subjects were Internet users who chose to respond to the question posted on the electronic edition of USA Today.

 What’s Wrong? In Exercises 25–28, identify what is wrong.

25. Potatoes In a poll sponsored by the Idaho Potato Commission, 1000 adults were asked to select their favorite vegetables, and the favorite choice was potatoes, which were selected by 26% of the respondents.
26. Healthy Water In a USA Today online poll, 951 Internet users chose to respond, and 57% of them said that they prefer drinking bottled water instead of tap water.

Percentages. In Exercises 29–36, answer the given questions, which are related to percentages.

 

  30. Checking Job Applicants In a study conducted by the Society for Human Resource Management, 347 human resource professionals were surveyed. Of those surveyed, 73% said that their companies conduct criminal background checks on all job applicants.

31. 1. What is the exact value that is 73% of the 347 survey subjects?
    2. Could the result from part (a) be the actual number of survey subjects who said that their companies conduct criminal background checks on all job applicants? Why or why not?
    3. What is the actual number of survey subjects who said that their company conducts criminal background checks on all job applicants?
    4. Assume that 112 of the survey subjects are females. What percentage of those surveyed are females?
32. Chillax USA Today reported results from a Research Now for Keurig survey in which 1458 men and 1543 women were asked this: “In a typical week, how often can you kick back and relax?”
    1. Among the women, 19% responded with “rarely, if ever.” What is the exact value that is 19% of the number of women surveyed?
    2. Could the result from part (a) be the actual number of women who responded with “rarely, if ever”? Why or why not?
    3. What is the actual number of women who responded with “rarely, if ever”?
    4. Among the men who responded, 219 responded with “rarely, if ever.” What is the percentage of men who responded with “rarely, if ever.”?
    5. Consider the question that the subjects were asked. Is that question clear and unambiguous so that all respondents will interpret the question the same way? How might the survey be improved?

 

Sec 1-2: ##

1.  Parameter and Statistic In a Harris Interactive survey of 2276 adults in the United States, it was found that 33% of those surveyed never travel using commercial airlines. Identify the population and sample. Is the value of 33% a statistic or a parameter?
2. Quantitative/Categorical Data Identify each of the following as quantitative data or categorical data.
   1. The platelet counts in Data Set 1 “Body Data” in Appendix B
   2. The cigarette brands in Data Set 13 “Cigarette Contents” in Appendix B
   3. The colors of the M&M candies in Data Set 27 “M&M Weights” in Appendix B
   4. The weights of the M&M candies in Data Set 27 “M&M Weights” in Appendix B
3. Discrete/Continuous Data Which of the following describe discrete data?
   1. The numbers of people surveyed in each of the next several years for the National Health and Nutrition Examination Surveys
   2. The exact foot lengths (measured in cm) of a random sample of statistics students
   3. The exact times that randomly selected drivers spend texting while driving during the past 7 days
4. Health Survey In a survey of 1020 adults in the United States, 44% said that they wash their hands after riding public transportation (based on data from KRC Research).
   1. Identify the sample and population.
   2. Is the value of 44% a statistic or parameter?
   3. What is the level of measurement of the value of 44%? (nominal, ordinal, interval, ratio)
   4. Are the numbers of subjects in such surveys discrete or continuous?

In Exercises 5–12, identify whether the given value is a statistic or a parameter.

5. On-time Flights In a study of American Airlines flights from JFK in New York to LAX in Los Angeles, 48 flights are randomly selected and the average (mean) arrival time is 8.9 minutes late.
6. CHIS A recent California Health Interview Survey (CHIS) included 2799 adolescent residents of California.

In Exercises 13–20, determine whether the data are from a discrete or continuous data set.

 

15. McDonald’s In a study of service times at a McDonald’s drive-up window, the numbers of cars serviced each hour of several days are recorded.

20. Texting Fatalities The Insurance Institute for Highway Safety collects data consisting of the numbers of motor vehicle fatalities caused by driving while texting.

In Exercises 21–28, determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate.

21. College Rankings U.S. News & World Report periodically provides its rankings of national universities, and in a recent year the ranks for Princeton, Harvard, and Yale were 1, 2, and 3, respectively.

24. Fast Food Service Times In a study of fast food service times, a researcher records the time intervals of drive-up customers beginning when they place their order and ending when they receive their order.

26.Movie Ratings The author rated the movie Star Wars: The Force Awakens with 5 stars on a scale of 5 stars.

28.Body Temperatures Body temperatures (in degrees Fahrenheit) listed in Data Set 3 “Body Temperatures” 

 

				Temperature Day 1		Temperature Day 2
Subject	Age	Sex	Smoke	8 AM	12 AM	8 AM	12 AM
1	22	M	Y	98.0	98.0	98.0	98.6
2	23	M	Y	97.0	97.6	97.4
3	22	M	Y	98.6	98.8	97.8	98.6
Body Temperatures (in degrees Fahrenheit) of Healthy Adults

In Exercises 29–32, identify the level of measurement of the data as nominal, ordinal, interval, or ratio. Also, explain what is wrong with the given calculation.

30.Social Security Numbers As part of a project in a statistics class, students report the last four digits of their Social Security numbers, and the average (mean) of those digits is computed to be 4.7.

 

32.College Ranks As of this writing, U.S. News & World Reportranked national universities, including these results: Princeton (1), Harvard (2), Yale (3), and Columbia (4). The difference between Princeton and Harvard is the same as the difference between Yale and Columbia.

 

Sec 1-3: 

 

 Exercises 5–8 refer to the study of an association between which ear is used for cell phone calls and whether the subject is left-handed or right-handed. The study is reported in “Hemispheric Dominance and Cell Phone Use,” by Seidman et al., JAMA Otolaryngology— Head & Neck Surgery, Vol. 139, No. 5. The study began with a survey e-mailed to 5000 people belonging to an otology online group, and 717 surveys were returned. (Otology relates to the ear and hearing.)

 

6.Experiment or Observational Study Is the study an experiment or an observational study? Explain.

8.Sampling Method Assume that the population consists of all students currently in your statistics class. Describe how to obtain a sample of six students so that the result is a sample of the given type.

1. 1. Simple random sample
   2. Systematic sample
   3. Stratified sample
   4. Cluster sample

In Exercises 9–20, identify which of these types of sampling is used: random, systematic, convenience, stratified, or cluster.

 

10.Sexuality of Women The sexuality of women was discussed in Shere Hite’s book Women and Love: A Cultural Revolution. Her conclusions were based on sample data that consisted of 4500 mailed responses from 100,000 questionnaires that were sent to women.

13.Driving A student of the author conducted a survey on driving habits by randomly selecting three different classes and surveying all of the students as they left those classes.

15.Dictionary The author collected sample data by randomly selecting five books from each of the categories of science, fiction, and history. The numbers of pages in the books were then identified.

18.Exit Polls During the last presidential election, CNN conducted an exit poll in which specific polling stations were randomly selected and all voters were surveyed as they left the premises.

Critical Thinking: What’s Wrong? In Exercises 21–28, determine whether the study is an experiment or an observational study, and then identify a major problem with the study.

21. Online News In a survey conducted by USA Today, 1465 Internet users chose to respond to this question posted on the USA Todayelectronic edition: “Is news online as satisfying as print and TV news?” 52% of the respondents said “yes.”
22. Physicians’ Health Study The Physicians’ Health Study involved 22,071 male physicians. Based on random selections, 11,037 of them were treated with aspirin and the other 11,034 were given placebos. The study was stopped early because it became clear that aspirin reduced the risk of myocardial infarctions by a substantial amount.
23. Drinking and Driving A researcher for a consortium of insurance companies plans to test for the effects of drinking on driving ability by randomly selecting 1000 drivers and then randomly assigning them to two groups: One group of 500 will drive in New York City after no alcohol consumption, and the second group will drive in New York City after consuming three shots of Jim Beam bourbon whiskey.

 

Ch.2

Sec 2-1: 

 

 

Time (sec)	Frequency
?60–119	?7
120–179	22
180–239	14
240–299	?2
300–359	?5
table for Exercise 1 mcdonald’s dinner service times

1. McDonald’s Dinner Service Times Refer to the accompanying frequency distribution. What problem would be created by using classes of 60–120, 120–180, . . ., 300–360?
2. Relative Frequency Distribution Use percentages to construct the relative frequency distribution corresponding to the accompanying frequency distribution for McDonald’s dinner times?

In Exercises 5–8, identify the class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. The frequency distributions are based on real data from Appendix B.

5.  

Age (yr) of Best Actress When Oscar Was Won	Frequency
20–29	29
30–39	34
40–49	14
50–59	?3
60–69	?5
70–79	?1
80–89	?1

 

Constructing Frequency Distributions. In Exercises 11–18, use the indicated data to construct the frequency distribution. (The data for Exercises 13–16 can be downloaded at TriolaStats.com.)

11. Old Faithful Listed below are sorted duration times (seconds) of eruptions of the Old Faithful geyser in Yellowstone National Park. Use these times to construct a frequency distribution. Use a class width of 25 seconds and begin with a lower class limit of 125 seconds.

125	203	205	221	225	229	233	233	235	236	236	237	238	238	239	240	240
240	240	241	241	242	242	242	243	243	244	245	245	245	245	246	246	248
248	248	249	249	250	251	252	253	253	255	255	256	257	258	262	264

 

17Analysis of Last Digits Heights of statistics students were obtained by the author as part of an experiment conducted for class. The last digits of those heights are listed below. Construct a frequency distribution with 10 classes. Based on the distribution, do the heights appear to be reported or actually measured? What do you know about the accuracy of the results?

0000000001123334555555555555555668889

 

Cumulative Frequency Distributions. In Exercises 21 and 22, construct the cumulative frequency distribution that corresponds to the frequency distribution in the exercise indicated.

21. Exercise 5 (Age of Best Actress When Oscar Was Won)

Age (yr) of Best Actress When Oscar Was Won	Frequency
20–29	29
30–39	34
40–49	14
50–59	?3
60–69	?5
70–79	?1
80–89	?1

Sec 2-2: 

 

1. Heights Heights of adult males are normally distributed. If a large sample of heights of adult males is randomly selected and the heights are illustrated in a histogram, what is the shape of that histogram?

 

Interpreting a Histogram. In Exercises 5–8, answer the questions by referring to the following Minitab-generated histogram, which depicts the weights (grams) of all quarters listed in Data Set 29 “Coin Weights” in Appendix B. (Grams are actually units of mass and the values shown on the horizontal scale are rounded.)

 

 

 

5. Sample Size What is the approximate number of quarters depicted in the three bars farthest to the left?
6. Class Width and Class Limits Give the approximate values of the class width, and the lower and upper class limits of the class depicted in the bar farthest to the left.
7. Relative Frequency Histogram How would the shape of the histogram change if the vertical scale uses relative frequencies expressed in percentages instead of the actual frequency counts as shown here?

 

Constructing Histograms. In Exercises 9–16, construct the histograms and answer the given questions.

9. Old Faithful Use the frequency distribution from Exercise11 in Section 2-1 on page 49 to construct a histogram. Does it appear to be the graph of data from a population with a normal distribution?
10. Tornadoes Use the frequency distribution from Exercise12 in Section 2-1 on page 49 to construct a histogram. Does the histogram appear to be skewed? If so, identify the type of skewness.
11. Burger King Lunch Service Times Use the frequency distribution from Exercise 13 in Section 2-1 on page 49to construct a histogram. Does the histogram appear to be skewed? If so, identify the type of skewness

 

 

 

  

Sec 2-3: 

 

Stemplots. In Exercises 7 and 8, construct the stemplot.

 

7. Pulse Rates Refer to the data listed in Exercise 5. How are the data sorted in the stemplot?

 

Time-Series Graphs. In Exercises 9 and 10, construct the time-series graph.

9. Gender Pay Gap Listed below are women’s median earnings as a percentage of men’s median earnings for recent years beginning with 1990. Is there a trend? How does it appear to affect women?

71.6	69.9	70.8	71.5	72.0	71.4	73.8	74.2	73.2	72.3	73.7
76.3	76.6	75.5	76.6	77.0	76.9	77.8	77.1	77.0	77.4	77.0

 

 

Pareto Charts. In Exercises 11 and 12 construct the Pareto chart.

12.Getting a Job In a survey, subjects seeking a job were asked to whom they should send a thank-you note after having a job interview. Results were as follows: 40 said only the person they spent the most time with, 396 said everyone they met, 40 said only the most senior-level person, 15 said the person that they had the best conversation with, and 10 said that they don’t send thank-you notes (based on data from TheLadders.com). Comment on the results.

 

Pie Charts. In Exercises 13 and 14, construct the pie chart

 

14. Getting a Job Use the data from Exercise 12 “Getting a Job.”

 

 

 

 

Ch.3

Sec 3-1:

 

1. Average The defunct website IncomeTaxList.com listed the “average” annual income for Florida as $35,031. What is the role of the term average in statistics? Should another term be used in place of average?
2. What’s Wrong? USA Today published a list consisting of the state tax on each gallon of gas. If we add the 50 state tax amounts and then divide by 50, we get 27.3 cents. Is the value of 27.3 cents the mean amount of state sales tax paid by all U.S. drivers? Why or why not?

Critical Thinking. For Exercises 5–20, watch out for these little buggers. Each of these exercises involves some feature that is somewhat tricky. Find the (a) mean, (b) median, (c) mode, (d) midrange, and then answer the given question.

 

5. Football Player Weights Listed below are the weights in pounds of 11 players randomly selected from the roster of the Seattle Seahawks when they won Super Bowl XLVIII (the same players from the preceding exercise). Are the results likely to be representative of all National Football League (NFL) players?

189,254,235,225,190,305,195,202,190,252,305

9.Hurricanes Listed below are the numbers of Atlantic hurricanes that occurred in each year. The data are listed in order by year, starting with the year 2000. What important feature of the data is not revealed by any of the measures of center?

8,9,8,7,9,15,5,6,8,4,12,7,8,2

 

19.California Smokers In the California Health Interview Survey, randomly selected adults are interviewed. One of the questions asks how many cigarettes are smoked per day, and results are listed below for 50 randomly selected respondents. How well do the results reflect the smoking behavior of California adults?

9	10	10	20	40	50	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
0	0	0	0	0

In Exercises 21–24, find the mean and median for each of the two samples, then compare the two sets of results.

 

 

22.Parking Meter Theft Listed below are amounts (in millions of dollars) collected from parking meters by Brinks and others in New York City during similar time periods. A larger data set was used to convict five Brinks employees of grand larceny. The data were provided by the attorney for New York City, and they are listed on the Data and Story Library (DASL) website. Do the limited data listed here show evidence of stealing by Brinks employees?

Collection Contractor Was Brinks	1.3	1.5	1.3	1.5	1.4	1.7	1.8	1.7	1.7	1.6
Collection Contractor Was Not Brinks	2.2	1.9	1.5	1.6	1.5	1.7	1.9	1.6	1.6	1.8

 

 

 

 

In Exercises 29–32, find the mean of the data summarized in the frequency distribution. Also, compare the computed means to the actual means obtained by using the original list of data values, which are as follows: (Exercise 29) 36.2 years; (Exercise 30) 44.1 years; (Exercise31) 224.3; (Exercise 32) 255.1.

29.  

Age (yr) of Best Actress When Oscar Was Won	Frequency
20–29	29
30–39	34
40–49	14
50–59	3
60–69	5
70–79	1
80–89	1

 

Sec 3-2: 

 

1. Range Rule of Thumb for Interpreting s The 20 brain volumes (cm³) from Data Set 8 “IQ and Brain Size” in AppendixB have a mean of 1126.0 cm³ and a standard deviation of 124.9 cm³. Use the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a brain volume of 1440 cm³ be significantly high?
2. Variance The 20 subjects used in Data Set 8 “IQ and Brain Size” in Appendix B have weights with a standard deviation of 20.0414 kg. What is the variance of their weights? Be sure to include the appropriate units with the result.

In Exercises 5–20, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-1, where we found measures of center. Here we find measures of variation.) Then answer the given questions.

5. Football Player Numbers Listed below are the jersey numbers of 11 players randomly selected from the roster of the Seattle Seahawks when they won Super Bowl XLVIII. What do the results tell us?

89,91,55,7,20,99,25,81,19,82,60

6. Football Player Weights Listed below are the weights in pounds of 11 players randomly selected from the roster of the Seattle Seahawks when they won Super Bowl XLVIII (the same players from the preceding exercise). Are the measures of variation likely to be typical of all NFL players?

189,254,235,225,190,305,195,202,190,252,305

 

13.Caffeine in Soft Drinks Listed below are measured amounts of caffeine (mg per 12oz of drink) obtained in one can from each of 20 brands (7-UP, A&W Root Beer, Cherry Coke, . . ., Tab). Are the statistics representative of the population of all cans of the same 20 brands consumed by Americans?

0 0 34 34 34 45 41 51 55 36 47 41 0 0 53 54 38 0 41 47

 

In Exercises 21–24, find the coefficient of variation for each of the two samples; then compare the variation. (The same data were used in Section 3-1.)

21. Blood Pressure A sample of blood pressure measurements is taken from Data Set 1 “Body Data” in Appendix B, and those values (mm Hg) are listed below. The values are matched so that 10 subjects each have a systolic and diastolic measurement.

Systolic:	118	128	158	96	156	122	116	136	126	120
Diastolic:	?80	?76	?74	?52	?90	?88	?58	?64	?72	?82

 

24. Bank Queues Waiting times (in seconds) of customers at the Madison Savings Bank are recorded with two configurations: single customer line; individual customer lines.

Single Line	390	396	402	408	426	438	444	462	462	462
Individual Lines	252	324	348	372	402	462	462	510	558	600

 

 

Identifying Significant Values with the Range Rule of Thumb.  In Exercises 33–36, use the range rule of thumb to identify the limits separating values that are significantly low or significantly high.

33. Pulse Rates of Females Based on Data Set 1 “Body Data” in Appendix B, females have pulse rates with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minute. Is a pulse rate of 44 beats per minute significantly low or significantly high? (All of these pulse rates are measured at rest.)

 

 

Sec 3-3: 

 

2.Heights The boxplot shown below results from the heights (cm) of males listed in Data Set 1 “Body Data” in Appendix B. What do the numbers in that boxplot tell us?

 

 

 

3.Boxplot Comparison Refer to the boxplots shown below that are drawn on the same scale. One boxplot represents weights of men, and the other boxplot represents weights of women. Which boxplot represents weights of women? Explain.

 

 

 

z Scores. In Exercises 5–8, express all z scores with two decimal places.

7.Female Pulse Rates Pulse rates of adult females are listed in Data Set 1 “Body Data” in Appendix B. The lowest pulse rate is 36 beats per minute, the mean of the listed pulse rates is 

x¯=74.0

 beats per minute, and their standard deviation is s = 12.5 beats per minute.

1. 1. What is the difference between the pulse rate of 36 beats per minute and the mean pulse rate of the females?
   2. How many standard deviations is that [the difference found in part (a)]?
   3. Convert the pulse rate of 36 beats per minutes to a zscore.
   4. If we consider pulse rates that convert to z scores between −2 and 2 to be neither significantly low nor significantly high, is the pulse rate of 36 beats per minute significant?

Significant Values. In Exercises 9 –12, consider a value to be significantly low if its z score is less than or equal to −2 or consider the value to be significantly high if its z score is greater than or equal to 2.

10.MCAT In a recent year, scores on the Medical College Admission Test (MCAT) had a mean of 25.2 and a standard deviation of 6.4. Identify the MCAT scores that are significantly low or significantly high.

Comparing Values. In Exercises 13–16, use z scores to compare the given values.

14.Red Blood Cell Counts Based on Data Set 1 “Body Data” in Appendix B, males have red blood cell counts with a mean of 4.719 and a standard deviation of 0.490, while females have red blood cell counts with a mean of 4.349 and a standard deviation of 0.402. Who has the higher count relative to the sample from which it came: a male with a count of 5.58 or a female with a count of 5.23? Explain.

15.Birth Weights Based on Data Set 4 “Births” in Appendix B, newborn males have weights with a mean of 3272.8 g and a standard deviation of 660.2 g. Newborn females have weights with a mean of 3037.1 g and a standard deviation of 706.3 g. Who has the weight that is more extreme relative to the group from which they came: a male who weighs 1500 g or a female who weighs 1500 g?

Boxplots. In Exercises 29–32, use the given data to construct a boxplot and identify the 5-number summary.

 

30.Cell Phone Radiation Listed below are the measured radiation absorption rates (in W/kg) corresponding to these cell phones: iPhone 5S, BlackBerry Z30, Sanyo Vero, Optimus V, Droid Razr, Nokia N97, Samsung Vibrant, Sony Z750a, Kyocera Kona, LG G2, and Virgin Mobile Supreme. The data are from the Federal Communications Commission.

1.18, 1.41, 1.49, 1.04, 1.45, 0.74,0.89, 1.42, 1.45, 0.51, 1.38

32.Blood Pressure Measurements Fourteen different second-year medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic readings (mm Hg) are listed below.

138,130,135,140,120,125,120,130,144,143,140,130,150