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Statistics The Exploration And Analysis Of Data 6th Edition John M Scheb, Jay Devore, Roxy Peck - Solutions
=+.031 are really considering different situations. Explain why it is plausible that both probabilities are correct.
=+6. Using basic probability rules, we can calculate that the probability that a player of this skill level is successful on the next 5 free throw attempts is which is relatively small. At first, this value might seem inconsistent with your answer in Step 5, but the estimated probability from Step
=+5. Use the combined class data to estimate the probability that a player of this skill level has a streak of at least 5 somewhere in a sequence of 50 free throw attempts.
=+4. Based on the graph from Step 3, does it appear likely that a player of this skill level would have a streak of 5 or more successes sometime during a sequence of 50 free throw attempts? Justify your answer based on the graph from Step 3.
=+3. Combine your longest streak value with those from the rest of the class, and construct a histogram or dotplot of these longest streak values.
=+2. For your sequence of 50 tosses, identify the longest streak by looking for the longest string of heads in your sequence. Determine the length of this longest streak.
=+1. Begin by simulating a sequence of 50 free throws for this player. Because this player has a probability of success 5 .5 for each attempt and the attempts are independent, we can model a free throw by tossing a coin.Using heads to represent a successful free throw and tails to represent a
=+Background: Consider a mediocre basketball player who has consistently made only 50% of his free throws over several seasons. If we were to examine his free throw record over the last 50 free throw attempts, is it likely that we would see a “streak” of 5 in a row where he is successful in
=+4. Working with a partner, write a paragraph explaining why European sports fans should or should not be worried by the results of the Polish experiment. Your explanation should be based on the observed proportion of heads from the Polish experiment and the graphical display constructed in Step 3.
=+3. Form a data set that consists of the values for proportion of heads observed in 250 tosses of a fair coin for the entire class. Summarize this data set by constructing a graphical display.
=+2. For your sequence of 250 tosses, calculate the proportion of heads observed.
=+1. For this first step, you can either (a) flip a U.S. penny 250 times, keeping a tally of the number of heads and tails observed (this won’t take as long as you think) or (b) simulate 250 coins tosses by using your calculator or a statistics software package to generate random numbers (if
=+In this activity, we will investigate whether this difference should be cause for alarm by examining whether observing 140 heads out of 250 tosses is an unusual outcome if the coin is fair.
=+A group in Poland claims that the Belgium-minted Euro does not have an equal chance of landing heads or tails. This claim was based on 250 tosses of the Belgium Euro, of which 140 (56%) came up heads. Should this be cause for alarm for European sports fans, who know that“important” decisions
=+Background: The New Scientist (January 4, 2002)reported on a controversy surrounding the new Euro coins that have been introduced as a common currency across most of Europe. Each country mints its own coins, but these coins are accepted in any of the countries that have adopted the Euro as its
=+Do you think that a Hershey’s Kiss is equally likely to land on its base or its side? Explain.
=+Working as a class, develop a plan for a simulation that would enable you to estimate this probability.Once you have an acceptable plan, carry out the simulation and use it to produce an estimate of the desired probability.
=+Background: The paper “What is the Probability of a Kiss? (It’s Not What You Think)” (found in the online Journal of Statistics Education [2002]) posed the following question: What is the probability that a Hershey’s Kiss will land on its base (as opposed to its side) if it is flipped
=+b. Compare the probability from Part (a) to the one computed in Exercise 6.26. Which decrease in the probability of on-time completion (Maria’s or Jacob’s) made the biggest change in the probability that the project is completed on time?
=+a. Use simulation (with at least 20 trials) to estimate the probability that the project is completed on time.
=+6.27 Refer to Exercises 6.25 and 6.26. Suppose that the probabilities of timely completion are as in Exercise 6.25 for Maria, Alex, and Juan but that Jacob has a probability of completing on time of .7 if Juan is on time and .5 if Juan is late.
=+6.26 In Exercise 6.25, the probability that Maria completes her part on time was .8. Suppose that this probability is really only .6. Use simulation (with at least 20 trials)to estimate the probability that the project is completed on time.
=+on time and 9 and 0 could represent late. Depending on what happened with Maria (late or on time), you would then look at the digit representing Alex’s part. If Maria was on time, 1–9 would represent on time for Alex, but if Maria was late, only 1–6 would represent on time. The parts for
=+probability that the project is completed on time. Think carefully about this one. For example, you might use a random digit to represent each part of the project (four in all). For the first digit (Maria’s part), 1–8 could represent
=+4. If Juan completes his part on time, the probability that Jacob completes on time is .9, but if Juan is late, the probability that Jacob completes on time is only .7.Use simulation (with at least 20 trials) to estimate the
=+3. If Alex completes his part on time, the probability that Juan completes on time is .8, but if Alex is late, the probability that Juan completes on time is only .5.
=+1. The probability that Maria completes her part on time is .8.2. If Maria completes her part on time, the probability that Alex completes on time is .9, but if Maria is late, the probability that Alex completes on time is only .6.
=+Because of the way the tasks have been divided, one student must finish before the next student can begin work. To ensure that the project is completed on time, a timeline is established, with a deadline for each team member. If any one of the team members is late, the timely completion of the
=+6.25 Four students must work together on a group project.They decide that each will take responsibility for a particular part of the project, as follows:Person Maria Alex Juan Jacob Task Survey Data Analysis Report design collection writing
=+b. Do you think that this is a fair way of distributing licenses? Can you propose an alternative procedure for distribution?
=+a. An individual who wishes to be an independent driver has put in a request for a single license. Use simulation to approximate the probability that the request will be granted. Perform at least 20 simulated lotteries (more is better!).
=+possible. For example, the city might fill requests for 2, 3, 1, and 3 licenses and then select a request for 3. Because there is only one license left, the last request selected would receive a license, but only one.
=+determine who gets the licenses, and no one may request more than three licenses. Twenty individuals and taxi companies have entered the lottery. Six of the 20 entries are requests for 3 licenses, 9 are requests for 2 licenses, and the rest are requests for a single license. The city will select
=+6.24 Many cities regulate the number of taxi licenses, and there is a great deal of competition for both new and existing licenses. Suppose that a city has decided to sell 10 new licenses for $25,000 each. A lottery will be held to
=+b. What is the probability that the researchers will incorrectly conclude that Treatment 2 is the better treatment?
=+a. What is the probability that more than 5 pairs must be treated before a conclusion can be reached? (Hint: P(more than 5) 5 1 2 P(5 or fewer).)
=+Treatment 1 and success for Treatment 2. Continue to select pairs, keeping track of the cumulative number of successes for each treatment. Stop the trial as soon as the number of successes for one treatment exceeds that for the other by 2. This would complete one trial. Now repeat this whole
=+a success and 8, 9, and 0 to indicate a failure. Let the second digit represent Treatment 2, with 1–4 representing a success. For example, if the two digits selected to represent a pair were 8 and 3, you would record failure for Bold exercises answered in back ● Data set available online
=+they might observe the results in the table on the next page. The chance experiment would stop after the sixth pair, because Treatment 1 has two more successes than Treatment 2. The researchers would conclude that Treatment 1 is preferable to Treatment 2.Suppose that Treatment 1 has a success
=+6.23 A medical research team wishes to evaluate two different treatments for a disease. Subjects are selected two at a time, and then one of the pair is assigned to each of the two treatments. The treatments are applied, and each is either a success (S) or a failure (F). The researchers keep
=+k. If two people are selected at random from this region, what is the probability that both are from different racial/ethnic groups?
=+j. If two people are selected at random from this region, what is the probability that both are residents of the same county?
=+i. If two people are selected at random from this region, what is the probability that exactly one is a Caucasian?
=+what is the probability that neither is Caucasian?
=+h. If two people are selected at random from this region,
=+what is the probability that both are Caucasians?
=+g. If two people are selected at random from this region,
=+what is the probability that the person is Asian or from San Luis Obispo County but not both?
=+f. If one person is selected at random from this region,
=+what is the probability that the person is either Asian or from San Luis Obispo County?
=+e. If one person is selected at random from this region,
=+what is the probability that the selected person is an Asian from San Luis Obispo County?
=+d. If one person is selected at random from this region,
=+c. If one Hispanic person is selected at random from this region, what is the probability that the selected individual is from Ventura?
=+what is the probability that the selected person is Hispanic?
=+b. If one person is selected at random from Ventura County,
=+a. If a census fact-checker selects one person at random from this region, what is the probability that the selected person is from Ventura County?
=+6.22 On April 1, 2000, the Bureau of the Census in the United States attempted to count every U.S. citizen and every resident. When counting such a large number of people, however, mistakes of various sorts are likely to arise. In 2000, many people were employed by the Bureau of the Census who
=+d. What is the probability that the selected student is a male who is not from the College of Agriculture?
=+c. What is the probability that the selected student is a male in the College of Agriculture?
=+b. What is the probability that the selected student is in the College of Agriculture?
=+a. What is the probability that the selected student is a male?
=+public university in the West. If we were to randomly select one student from this university:
=+6.21 ▼ The table below describes (approximately) the distribution of students by gender and college at a midsize Bold exercises answered in back ● Data set available online but not required ▼ Video solution available College Liberal Science and Gender Education Engineering Arts Math
=+f. Estimate the proportion of those first-year students with high school GPAs 3.5 and above who are on academic probation at the end of the first semester.
=+e. Estimate the proportion of first-year students with high school GPAs between 2.5 and 3.0 who are on academic probation at the end of the first semester.
=+d. Are the two outcomes selected student has a GPA of 3.5 or above and selected student is on academic probation at the end of the first semester independent outcomes?How can you tell?
=+c. What is the estimated probability that a randomly selected first-year student at this university had a high school GPA of 3.5 or above?
=+b. Use the table constructed in Part (a) to approximate the probability that a randomly selected first-year student at this university will be on academic probation at the end of the first semester.
=+a. Construct a table of the estimated probabilities for each GPA–probation combination by dividing the number of students in each of the 6 cells of the table by 500.
=+6.20 Five hundred first-year students at a state university were classified according to both high school grade point average (GPA) and whether they were on academic probation at the end of their first semester. The data are summarized in the accompanying table.High School GPA 2.5 to 3.0 to 3.5
=+d. The probability of on-time delivery nationwide
=+a. The probability of an on-time delivery in Los Angelesb. The probability of late delivery in Washington, D.C.c. The probability that both of two letters mailed in New York are delivered on time
=+the Price Waterhouse study were as follows (these numbers are fictitious, but they are compatible with summary values given in the article):Number Number of of Letters Letters Arriving Mailed on Time Los Angeles 500 425 New York 500 415 Washington, D.C. 500 405 Nationwide 6000 5220 Use the given
=+is promised for distances over 600 mi. The Price Waterhouse accounting firm conducted an independent audit by“seeding” the mail with letters and recording on-time delivery rates for these letters. Suppose that the results of
=+6.19 The Los Angeles Times (June 14, 1995) reported that the U.S. Postal Service is getting speedier, with higher overnight on-time delivery rates than in the past. Postal Service standards call for overnight delivery within a zone of about 60 mi for any first-class letter deposited by the last
=+4. Calculate the estimated probability by dividing the number of observations for which the outcome of interest occurred by the total number of observations generated.
=+3. Repeat Step 2 a large number of times.
=+2. Generate an observation using the method from Step 1, and determine whether the outcome of interest has occurred.
=+1. Design a method that uses a random mechanism (such as a random number generator or table, the selection of a ball from a box, or the toss of a coin) to represent an observation.Be sure that the important characteristics of the actual process are preserved.
=+c. If you are in the third priority group next term, is it likely that you will get more than 9 units during the first call? Explain.
=+b. Suppose that a student reports receiving 11 units during the first call. Is it more likely that he or she is in the first or the fourth priority group?
=+a. What proportion of students at this university got 10 or more units during the first call?
=+Number of Units Secured During First Call to Registration System Priority More Group 0–3 4–6 7–9 10–12 Than 12 1 .01 .01 .06 .10 .07 2 .02 .03 .06 .09 .05 3 .04 .06 .06 .06 .03 4 .04 .08 .07 .05 .01
=+6.18 Students at a particular university use a telephone registration system to select their courses for the next term. There are four different priority groups, with students in Group 1 registering first, followed by those in Group 2, and so on. Suppose that the university provided the
=+6.17 A Gallup Poll conducted in November 2002 examined how people perceived the risks associated with smoking. The following table summarizes data on smoking status and perceived risk of smoking that is consistent with summary quantities published by Gallup:Perceived Risk Some- Not Not Smoking
=+calculate estimates of any probabilities that are relevant to your justification.
=+The researchers drew the following conclusion: Women with children younger than age 6 are much more likely to be injured on the job than childless women or mothers with older children. Provide a justification for the researchers’ conclusion. Use the information in the table to
=+6.16 Researchers at UCLA were interested in whether working mothers were more likely to suffer workplace injuries than women without children. They studied 1400 working women, and a summary of their findings was reported in the San Luis Obispo Telegram-Tribune (February 28, 1995). The
=+Do you think ultrasound is equally reliable for predicting gender for boys and for girls? Explain, using the information in the table to calculate estimates of any probabilities that are relevant to your conclusion.
=+6.15 Is ultrasound a reliable method for determining the gender of an unborn baby? Consider the following data on 1000 births, which are consistent with summary values that appeared in the online Journal of Statistics Education(“New Approaches to Learning Probability in the First Statistics
=+b. Three different probability rules are used in the calculation of the Diversity Index: the Complement Rule, the Addition Rule, and the Multiplication Rule. Describe the way in which each is used.
=+a. What additional assumption about race must be made to justify use of the addition rule in the computation of as the probability that two randomly selected individuals are of the same race?
=+3. The calculation of the Diversity Index treats Hispanic ethnicity as if it were independent of race
=+2. is the probability that two randomly selected individuals are either both Hispanic or both not Hispanic
=+1. is the probability that two randomly selected individuals are the same race
=+American Indian, API is the event that a randomly selected individual is Asian or Pacific Islander, and H is the event that a randomly selected individual is Hispanic. The explanation of this index stated that
=+where W is the event that a randomly selected individual is white, B is the event that a randomly selected individual is black, AI is the event that a randomly selected individual is
=+6.14 USA Today (March 15, 2001) introduced a measure of racial and ethnic diversity called the Diversity Index.The Diversity Index is supposed to approximate the probability that two randomly selected individuals are racially or ethnically different. The equation used to compute the Diversity
=+e. How would the probability that the system works change if there were three components in series in each of the two subsystems?
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