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Diez et al - OpenIntro Statistics 3/e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 7 / 83

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

Last Saved : n/a Saving...  ()

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7/83 (8.4%)

  • Instructions

    WebAssign is proud to support the open source teaching community through our partnership with OpenIntro. OpenIntro Statistics, 3rd edition, by David M. Diez, Christopher D. Barr, and Mine Çetinkaya-Rundel, is a college-level textbook covering data basics, probability (optional), distributions, inference for means and proportions, and regression, including multiple and the basics of logistic regression. The WebAssign component for this title features an eBook, class analytics tools, and instant student feedback on questions.

    Question 1 is a probability question involving the game of roulette. Part (c) asks students to compare their confidence in their answers to parts (a) and (b) using a fill-in-the-blank sentence.

    Question 2 has students draw a Venn diagram to model the population overlap for Americans who live below the poverty line or who speak a language other than English at home in a 2010 survey by American Community Survey. Students are then asked a series of questions requiring them to analyze this distribution based on the information presented in the Venn diagram.

    Question 3 asks students to find conditional probabilities given a table displaying the probability distribution of health status and health coverage of respondents to a telephone survey conducted by the Behavioral Risk Factor Surveillance System. Students are then asked to determine whether the variables are independent.

    Question 4 has students find conditional probabilities given a table displaying the frequencies of eye color for males and females in heterosexual relationships. Students are then asked to determine whether the variables are independent.

    Questions 5 and 6 ask students to find the conditional probability that a given situation will occur based on given marginal and conditional probabilities.

    Questions 7 and 8 are a series of questions comparing two normal distributions of men and women racers in particular age ranges. Question 7 also asks students to reflect back on their results if the distributions weren't normal.

    Questions 9 and 10 focus on analyzing situations that are nearly normal and deriving conclusions based on the given mean and standard deviation.

    Questions 11 and 12 involve random samples of Americans and whether they have had chickenpox before adulthood. A series of questions are asked based on the binomial distribution and what conclusions can be made based on this information.

    Questions 13 and 14 are questions about the probability of events happening in a binomial distribution.

    Question 15 shows an example of an open-ended, manually-graded question that requires the student to outline the design for an experimental study. 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.

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.

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1. 5/5 points  |  Previous Answers DiezStat3 2.E.002. My Notes
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The game of roulette involves spinning a wheel with 38 slots: 18 red, 18 black, and 2 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball.
(a)
You watch a roulette wheel spin 4 consecutive times and the ball lands on a red slot each time. What is the probability that the ball will land on a red slot on the next spin? (Enter your probability as a fraction.)
Correct: Your answer is correct.
(b)
You watch a roulette wheel spin 400 consecutive times and the ball lands on a red slot each time. What is the probability that the ball will land on a red slot on the next spin? (Enter your probability as a fraction.)
Correct: Your answer is correct.
(c)
Are you equally confident of your answers to parts (a) and (b)? Why or why not?
Theoretically the probability in part (b) is Correct: Your answer is correct. , however it is very unlikely that a fair roulette wheel will land on a red slot 400 consecutive times. It is possible that the the wheel in part (b) has been rigged, and hence the probability of red might be Correct: Your answer is correct. the probability in part (a). We should be Correct: Your answer is correct. confident of the answer to part (b) than the answer to part (a).

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2. 1/11 points  |  Previous Answers DiezStat3 2.E.008. My Notes
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The American Community Survey is an ongoing survey that provides data every year to give communities the current information they need to plan investments and services. The 2010 American Community Survey estimates that 14.6% of Americans live below the poverty line, 20.7% speak a language other than English (foreign language) at home, and 4.2% fall into both categories.
(a)
Are living below the poverty line and speaking a foreign language at home disjoint?
     Correct: Your answer is correct.
(b)
Draw a Venn diagram summarizing the variables and their associated probabilities. (Enter your answers to three decimal places.)
speak foreign language below poverty line Incorrect: Your answer is incorrect. Incorrect: Your answer is incorrect. Incorrect: Your answer is incorrect.
(c)
What percent of Americans live below the poverty line and only speak English at home? (Enter your answer to one decimal place.)
%
(d)
What percent of Americans live below the poverty line or speak a foreign language at home? (Enter your answer to one decimal place.)
%
(e)
What percent of Americans live above the poverty line and only speak English at home? (Enter your answer to one decimal place.)
%
(f)
Is the event that someone lives below the poverty line independent of the event that the person speaks a foreign language at home? (Enter your answers to four decimal places.)
Using the multiplication rule, P(below poverty line) × P(speak foreign language) = %, while P(below poverty line and speak foreign language) = %. Since these two values are , the events are .

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3. 1/7 points  |  Previous Answers DiezStat3 2.E.018. My Notes
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The Behavioral Risk Factor Surveillance System (BRFSS) is an annual telephone survey designed to identify risk factors in the adult population and report emerging health trends. The following table displays the distribution of health status of respondents to this survey (excellent, very good, good, fair, poor) and whether or not they have health insurance.
Health Status
Excellent Very Good Good Fair Poor Total
Health
Coverage 		No 0.0230 0.0361 0.0424 0.0199 0.0050 0.1264
Yes 0.2097 0.3122 0.2411 0.0805 0.0301 0.8736
Total 0.2327 0.3483 0.2835 0.1004 0.0351 1.0000
(a)
Are being in excellent health and having health coverage mutually exclusive?
     Correct: Your answer is correct.
(b)
What is the probability that a randomly chosen individual has excellent health? (Enter your answer to four decimal places.)
Incorrect: Your answer is incorrect.
(c)
What is the probability that a randomly chosen individual has excellent health given that he has health coverage? (Round your answer to two decimal places.)
(d)
What is the probability that a randomly chosen individual has excellent health given that he doesn't have health coverage? (Round your answer to two decimal places.)
(e)
Do having excellent health and having health coverage appear to be independent?
The probability that a person has excellent health between the two health coverage categories. So, since knowing something about someone's health coverage useful information in predicting whether the person has excellent health, the variables are .

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4. –/6 points DiezStat3 2.E.020. My Notes
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Assortative mating is a nonrandom mating pattern where individuals with similar genotypes and/or phenotypes mate with one another more frequently than what would be expected under a random mating pattern. Researchers studying this topic collected data on eye colors of 202 men and their female partners. The table below summarizes the results. For simplicity, we only include heterosexual relationships in this exercise. (Round your answers to four decimal places.)
Partner (female)
Blue Brown Green Total
Self (male) Blue 77 23 12 112
Brown 19 23 9 51
Green 11 7 21 39
Total 107 53 42 202
(a)
What is the probability that a randomly chosen male respondent or his partner has blue eyes?
(b)
What is the probability that a randomly chosen male respondent with blue eyes has a partner with blue eyes?
(c)
What is the probability that a randomly chosen male respondent with brown eyes has a partner with blue eyes?
What about the probability of a randomly chosen male respondent with green eyes having a partner with blue eyes?
(d)
Does it appear that the eye colors of male respondents and their partners are independent? Explain your reasoning.
It is for a man with blue eyes to have a partner with blue eyes than a man with another eye color to have a partner with blue eyes. Therefore it appears that eye colors of males and their partners are .

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5. –/1 points DiezStat3 2.E.022. My Notes
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A genetic test is used to determine if people have a predisposition for thrombosis, which is the formation of a blood clot inside a blood vessel that obstructs the flow of blood through the circulatory system. It is believed that 3% of people actually have this predisposition. The genetic test is 99% accurate if a person actually has the predisposition, meaning that the probability of a positive test result when a person actually has the predisposition is 0.99. The test is 98% accurate if a person does not have the predisposition. What is the probability that a randomly selected person who tests positive for the predisposition by the test actually has the predisposition? (Round your answer to four decimal places.)

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6. –/1 points DiezStat3 2.E.026. My Notes
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About 30% of human twins are identical, and the rest are fraternal. Identical twins are necessarily the same sex—half are males and the other half are females. One-quarter of fraternal twins are both male, one-quarter both female, and one-half are mixes: one male, one female. You have just become a parent of twins and are told they are both girls. Given this information, what is the probability that they are identical? (Round your answer to four decimal places.)

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7. –/18 points DiezStat3 3.E.004. My Notes
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In triathlons, it is common for racers to be placed into age and gender groups. Friends Leo and Mary both completed the Hermosa Beach Triathlon, where Leo competed in the Men, Ages 30–34 group while Mary competed in the Women, Ages 25–29 group. Leo completed the race in 1:25:28 (5128 seconds), while Mary completed the race in 1:32:56 (5576 seconds). Obviously Leo finished faster, but they are curious about how they did within their respective groups. Can you help them? Here is some information on the performance of their groups.
  • The finishing times of the Men, Ages 30–34 group has a mean of 4313 seconds with a standard deviation of 583 seconds.
  • The finishing times of the Women, Ages 25–29 group has a mean of 5261 seconds with a standard deviation of 807 seconds.
  • The distributions of finishing times for both groups are approximately Normal.
Remember: a better performance corresponds to a faster finish.
(a)
Write down the short-hand for these two normal distributions.
Men, Ages 30–34
N
μ = , σ =
Women, Ages 25–29
N
μ = , σ =
(b)
What are the Z-scores for Leo's and Mary's finishing times? (Round your answers to two decimal places.)
ZLeo = ZMary =
What do these Z-scores tell you?
Leo finished standard deviations the mean of his group's finishing time and Mary finished standard deviations the mean of her group's finishing time.
(c)
Did Leo or Mary rank better in their respective groups? Explain your reasoning.
Since a lower Z score indicates a finishing time, did better.
(d)
What percent of the triathletes did Leo finish faster than in his group? (Round your answer to two decimal places.)
%
(e)
What percent of the triathletes did Mary finish faster than in her group? (Round your answer to two decimal places.)
%
(f)
If the distributions of finishing times are not nearly normal, would your answers to parts (b)–(e) change? Explain your reasoning.
The answer to part (b) change, since Z scores be calculated for distributions that are not normal. The answers to parts (c)–(d) change, since we use the Z table to calculate probabilities and percentiles without a normal model.
You may need to use the appropriate table in the Appendix of Tables to answer this question.

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8. –/2 points DiezStat3 3.E.006. My Notes
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We have two distributions for triathlon times:
N(μ = 4314, σ = 582)
 for Men, Ages 30–34 and
N(μ = 5265, σ = 807)
 for the Women, Ages 25–29 group. Times are listed in seconds. Use this information to compute each of the following. (Round your answers to the nearest integer.)
(a)
the cutoff time for the fastest 5% of athletes in the men's group, i.e., those who took the shortest 5% of time to finish
sec
(b)
the cutoff time for the slowest 10% of athletes in the women's group
sec
You may need to use the appropriate table in the Appendix of Tables to answer this question.

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9. –/4 points DiezStat3 3.E.012. My Notes
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The distribution of passenger vehicle speeds traveling on a certain freeway in California is nearly normal with a mean of 73.6 miles/hour and a standard deviation of 4.73 miles/hour.
(a)
What percent of passenger vehicles travel slower than 80 miles/hour? (Round your answer to two decimal places.)
%
(b)
What percent of passenger vehicles travel between 60 and 80 miles/hour? (Round your answer to two decimal places.)
%
(c)
How fast do the fastest 5% of passenger vehicles travel? (Round your answer to four decimal places.)
mph
(d)
The speed limit on this stretch of the freeway is 70 miles/hour. Approximate what percentage of the passenger vehicles travel above the speed limit on this stretch of the freeway. (Round your answer to two decimal places.)
%
You may need to use the appropriate table in the Appendix of Tables to answer this question.

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10. –/7 points DiezStat3 3.E.018. My Notes
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Below are heights of 25 female college students.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
54 55 56 56 57 58 58 59 60 60 60 61 61 62 62 63 63 63 64 65 65 67 67 69 73
(a)
The mean height is 61.52 inches with a standard deviation of 4.58 inches. Use this information to determine if the heights approximately follow the 68-95-99.7% Rule. (Enter your answers to the nearest whole number.)
The percentage of heights within one standard deviation of the mean is %.
The percentage of heights within two standard deviations of the mean is %.
The percentage of heights within three standard deviations of the mean is %.
Therefore, the heights follow the 68-95-99.7% Rule.
(b)
Do these data appear to follow a normal distribution? Explain your reasoning using the graphs provided below.
The superimposed normal curve approximate the distribution well. The points on the normal probability plot follow a straight line. Therefore, the graphs indicate the data appear to be normal.

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11. –/9 points DiezStat3 3.E.026. My Notes
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The National Vaccine Information Center estimates that 90% of Americans have had chickenpox by the time they reach adulthood.
(a)
Determine if the use of the binomial distribution is appropriate for calculating the probability that exactly 94 out of 100 randomly sampled American adults had chickenpox during childhood.
The trials independent from one another. The number of trials fixed. There are possible outcomes for each trial. The probability of a success the same for each trial. Therefore, the binomial distribution be used.
(b)
Calculate the probability that exactly 94 out of 100 randomly sampled American adults had chickenpox during childhood. (Round your answer to four decimal places.)
(c)
What is the probability that exactly 6 out of a new sample of 100 American adults have not had chickenpox in their childhood? (Round your answer to four decimal places.)
(d)
What is the probability that at least 1 out of 10 randomly sampled American adults have had chickenpox? (Round your answer to four decimal places.)
(e)
What is the probability that at most 3 out of 10 randomly sampled American adults have not had chickenpox? (Round your answer to four decimal places.)

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12. –/7 points DiezStat3 3.E.028. My Notes
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About 90% of American adults had chickenpox before adulthood. We now consider a random sample of 150 American adults.
(a)
How many people in this sample would you expect to have had chickenpox in their childhood? (Enter your answer as a whole number.)
people
And with what standard deviation? (Round your answer to two decimal places.)
people
(b)
Would you be surprised if there were 134 people who have had chickenpox in their childhood? (Round your answer to two decimal places.)
Since
z = ,
 which is two standard deviations away from the mean, it surprising for there to be 134 people who have had chickenpox in childhood.
(c)
What is the probability that 134 or fewer people in this sample have had chickenpox in their childhood? (Round your answer to four decimal places.)
How does this probability relate to your answer to part (b)?
    
You may need to use the appropriate table in the Appendix of Tables to answer this question.

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13. –/1 points DiezStat3 3.E.030. My Notes
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Pew Research reported in 2012 that the typical response rate to their surveys is only 9%. If for a particular survey 12,000 households are contacted, what is the probability that at least 1,200 will agree to respond? (Round your answer to four decimal places.)
You may need to use the appropriate table in the Appendix of Tables to answer this question.

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14. –/3 points DiezStat3 3.E.036. My Notes
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In a multiple choice quiz there are 5 questions and 4 choices for each question (a, b, c, d). Robin has not studied for the quiz at all, and decides to randomly guess the answers. (Round your answers to four decimal places.)
(a)
What is the probability that the first question she gets right is the fifth question?
(b)
What is the probability that she gets exactly 4 or exactly 5 questions right?
(c)
What is the probability that she gets the majority of the questions right?

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15. –/1 points DiezStat3 1.E.034. My Notes
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You would like to conduct an experiment in class to see if students learn better if they study without any music, with music that has no lyrics (instrumental), or with music that has lyrics. Briefly outline a design for this study.

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