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Statistics The Art And Science Of Learning From Data 4th Global Edition Alan Agresti, Christine A. Franklin, Bernhard Klingenberg - Solutions
Find the necessary confidence interval for the population mean m. Interpret the interval that you have constructed. 13. a .01, n = 38, x=34, s2=12
Find the necessary confidence interval for the population mean m. Interpret the interval that you have constructed. 12. A 90% confidence interval, n = 50, x = 21.9, s = 3.44
Find the necessary confidence interval for the population mean m. Interpret the interval that you have constructed. 11. A 90% confidence interval, n = 125,=.84, s=.086
Find the necessary confidence interval for the population mean m. Interpret the interval that you have constructed. 10. A 95% confidence interval, n=64,x=2.73, s =.1047
Find the necessary confidence interval for the population mean m. Interpret the interval that you have constructed. 9. A 95% confidence interval, n = 36, x=13.1, s = 3.42
8. Confidence coefficient 1-a =.95 Find the z-values needed to calculate large-sample confidence intervals for the confidence levels
7. Confidence coefficient 1-a =.99 Find the z-values needed to calculate large-sample confidence intervals for the confidence levels
6. Confidence coefficient 1-a =.90 Find the z-values needed to calculate large-sample confidence intervals for the confidence levels
5. Confidence coefficient 1-a =.98 Find the z-values needed to calculate large-sample confidence intervals for the confidence levels
4. A 99% confidence interval Find the z-values needed to calculate large-sample confidence intervals for the confidence levels
3. A 98% confidence interval Find the z-values needed to calculate large-sample confidence intervals for the confidence levels
2. A 95% confidence interval Find the z-values needed to calculate large-sample confidence intervals for the confidence levels
1. A 90% confidence interval Find the z-values needed to calculate large-sample confidence intervals for the confidence levels
A random sample of 985 “likely” voters—those who are likely to vote in the upcoming election—were polled by the Republican Party. Of those surveyed, 592 indicated that they intended to vote for the Republican candidate in the upcoming election. Construct a 90%confidence interval for p, the
Construct a 99% confidence interval for the mean daily intake of dairy products for adult men in Example 8.6.
The average daily intake of dairy products for a random sample of n550 adult males was x 5756 grams per day with a standard deviation of s535 grams per day. Use this sample information to construct a 95% confidence interval for the mean daily intake of dairy products for men.
35. Hungry Rats In an experiment to assess the strength of the hunger drive in rats, 30 previously trained animals were deprived of food for 24 hours. At the end of the 24-hour period, each animal was put into a cage where food was dispensed if the animal pressed a lever. The length of time the
34. Men on Mars? Do you think that the United States should pursue a program to send humans to Mars? An opinion poll conducted by the Associated Press indicated that 49% of the 1034 adults surveyed think that we should pursue such a program.4a. Estimate the true proportion of Americans who think
33. “900” Numbers Radio and television stations often air controversial issues during broadcast time. A poll is then conducted, asking viewers who agree with the issue to call a certain 900 telephone number and those who disagree to call a second 900 telephone number.All respondents pay a fee
32. Hotel Costs Hotel costs during the summer months can vary substantially depending on the type of room and the amenities offered.3 Suppose that we randomly select 50 billing statements from each of the computer databases of the Marriott, Westin, and the Doubletree hotel chains, and record the
31. Multimedia Kids Do our children spend enough time enjoying the outdoors and playing with friends, or are they spending more time glued to the television, computer, and their cell phones? A random sample of 250 youth between the ages of 8 and 18 showed that 170 of them had a TV in their bedroom
30. Consumer Confidence An increase in the rate of consumer savings is frequently tied to a lack of confidence in the economy. A random sample of n5200 savings accounts in a local community showed a mean increase in savings account values of 7.2%over the past 12 months, with a standard deviation of
29. Biomass Biomass, the total amount of vegetation held by the earth’s forests, is important in determining the amount of unabsorbed carbon dioxide that is expected to remain in the earth’s atmosphere.2 Suppose a sample of 75 one-square-meter plots, randomly chosen in North America’s boreal
28. The San Andreas Fault A geologist studying the movement of the earth’s crust at a particular location on California’s San Andreas fault found many fractures in the local rock structure. In an attempt to determine the mean angle of the breaks, she sampled n550 fractures and found the sample
27. Specific Gravity If 36 measurements of the specific gravity of aluminum had a mean of 2.705 and a standard deviation of .028, find the point estimate for the actual specific gravity of aluminum and calculate the margin of error.
26. Recidivism An experimental rehabilitation technique was used on released convicts. It was shown that 79 of 121 men subjected to the technique pursued useful and crime-free lives for a 3-year period following prison release. Find a point estimate for p, the probability that a convict subjected
25. Antibiotics You want to estimate the mean hourly yield for a process that manufactures an antibiotic. You observe the process for 100 hourly periods chosen at random, with the results x 51020 grams per hour and s590. Estimate the mean hourly yield for the process and calculate the margin of
24. Suppose you are writing a questionnaire for a sample survey involving n=100 individuals, which will generate estimates for several different binomial proportions. If you want to report a single margin of error for the survey, what margin of error should you use? give the best point estimate for
23. A random sample of n=500 observations from a binomial population produced x=450 successes. give the best point estimate for the binomial proportion p and calculate the margin of error.
22. A random sample of n=900 observations from a binomial population produced x=655 successes. give the best point estimate for the binomial proportion p and calculate the margin of error.
21. A random sample of n575 observations from a quantitative population produced x =29.7 and s2 =510.8 give the best point estimate for the population mean m and calculate the margin of error.
20. A random sample of n550 observations from a quantitative population produced x =556.4 and s2 =2.6. give the best point estimate for the population mean m and calculate the margin of error.
Calculate the margin of error in estimating a binomial proportion p using samples of size n=100 and the values of p given What value of p produces the largest margin of error? 19. p=.9
Calculate the margin of error in estimating a binomial proportion p using samples of size n=100 and the values of p given What value of p produces the largest margin of error? 18. p=.7
Calculate the margin of error in estimating a binomial proportion p using samples of size n=100 and the values of p given What value of p produces the largest margin of error? 17. p=.5
Calculate the margin of error in estimating a binomial proportion p using samples of size n=100 and the values of p given What value of p produces the largest margin of error? 16. p=.3
Calculate the margin of error in estimating a binomial proportion p using samples of size n=100 and the values of p given What value of p produces the largest margin of error? 15. p=.1
Calculate the margin of error in estimating a binomial proportion p for the sample sizes given . Use p=.5 to calculate the standard error of the estimator, and comment on how an increased sample size affects the margin of error 14. n=1000
Calculate the margin of error in estimating a binomial proportion p for the sample sizes given . Use p=.5 to calculate the standard error of the estimator, and comment on how an increased sample size affects the margin of error 13. n=400
Calculate the margin of error in estimating a binomial proportion p for the sample sizes given . Use p=.5 to calculate the standard error of the estimator, and comment on how an increased sample size affects the margin of error 12. n=100
Calculate the margin of error in estimating a binomial proportion p for the sample sizes given . Use p=.5 to calculate the standard error of the estimator, and comment on how an increased sample size affects the margin of error 11. n=30
Calculate the margin of error in estimating a population mean m for the values given . Comment on how an increased sample size affects the margin of error 10. n 1000, s2=4
Calculate the margin of error in estimating a population mean m for the values given . Comment on how an increased sample size affects the margin of error n = 500, s=4 9. n=
Calculate the margin of error in estimating a population mean m for the values given . Comment on how an increased sample size affects the margin of error 8. n=100, s=4
Calculate the margin of error in estimating a population mean m for the values given . Comment on how an increased sample size affects the margin of error 7. n=50,s=4
Calculate the margin of error in estimating a population mean m for the values given. Comment on how a larger population variance affects the margin of error. 6. n=30,0 = 3.8
Calculate the margin of error in estimating a population mean m for the values given. Comment on how a larger population variance affects the margin of error. 5. n 30, 1.5
Calculate the margin of error in estimating a population mean m for the values given. Comment on how a larger population variance affects the margin of error. 4. n = 30,0=9
Calculate the margin of error in estimating a population mean m for the values given. Comment on how a larger population variance affects the margin of error. 3. n=30,0 = 2
In addition to the average weight of the Arctic polar bear, the scientist in Example 8.4 is also interested in the opinions of adults on the subject of global warming. He selects a random sample of n5100 adults, and finds that 73% of the sampled adults think global warming is a very serious
A scientist is studying a species of polar bear, found in and around the Arctic Ocean. Their range is limited by the availability of sea ice, which they use as a platform to hunt seals, the mainstay of their diet. The destruction of its habitat on the Arctic ice, which has been attributed to global
A veterinarian wants to estimate the average weight gain per month of 4-month-old golden retriever pups when placed on a lamb and rice diet. The population consists of the weight gains per month of all 4-month-old golden retriever pups that could be given this particular diet. The veterinarian
The supervisor in Example 8.1 is told by the plant owner that the thickness of the copper plating must not be less than .025 millimeter in order for the process to be in control. To decide whether or not the process is in control, the supervisor might devise a test. He could hypothesize (or assume)
The circuits in computers and other electronics equipment consist of one or more printed circuit boards (PCBs). In order to find the proper setting of a plating process applied to one side of a PCB, a production supervisor might estimate the average thickness of copper plating on PCBs using samples
5.6 Pick the incorrect statement Which of the following statements is not correct, and why?a. If the number of male and female employees at a call center is equal, then the probability that a call is answered by a female employee is 0.50.b. If you randomly generate 10 digits, each integer between 0
Airline overbooking For the Boston to Chicago route, an airline flies a Boeing 737–800 with 170 seats. Based on past experience, the airline finds that people who purchase a ticket for this flight have 0.80 probability of showing up for the flight. They routinely sell 190 tickets for the flight,
Stock market randomness Based on the previous exercise and what you have learned in this and the previous chapter (for example, Exercise 5.12), if you are a serious investor, explain why you should not get too excited if sometime in the next year the stock market goes up for seven days in a row.
6.86 Longest streak made In basketball, when the probability of making a free throw is 0.50 and successive shots are independent, the probability distribution of the longest streak of shots made has m = 4 for 25 shots, m = 5 for 50 shots, m = 6 for 100 shots, and m = 7 for 200 shots.a. How does the
6.85 Family size in Gaza The Palestinian Central Bureau of Statistics (www.pcbs.gov.ps) asked mothers of age 20–24 about the ideal number of children. For those living on the Gaza Strip, the probability distribution is approximately P112 = 0.01, P122 = 0.10, P132 = 0.09, P142 = 0.31, P152 = 0.19,
6.84 More best of five Refer to the previous exercise which asked for the distribution of the number of games played in a best of 5 series when team A wins with probability 50%.a. Find the expected number of games played in a best of five series.b. Find the expected number of games played when team
6.82 Which distribution for sales? A salesperson uses random digit dialing to call people and try to interest them in applying for a charge card for a large department store chain. From past experience, she is successful on 2% of her calls. In a typical working day, she makes 200 calls.Let X be the
Survival A cohort life table is used to represent the overall mortality rate of the entire lifetime of a certain population.Assume the number of people who survived until the age of 1 in a certain cohort is 98500 with a probability of death of 0.0002 between the ages of 1 and 4.a. Find the expected
Likes on Facebook A large retail chain sends out an ad about a new product to 15 million users on Facebook and asks them to like the message. Assume the probability that a user will like the message (instead of ignoring it) is 0.00001.a. State assumptions for a binomial distribution to apply for X
Total loss A total-loss insurance policy pays $15,000 against a premium of $500 if a car is considered a total loss. A company estimates that for such policies, the probability a car is considered a total loss is 0.0015. In a portfolio of n policies of this type, let X be the number of total loss
Dating success Based on past experience, Julio believes he has a 60% chance of success when he calls a woman and asks for a date.a. State assumptions needed for the binomial distribution to apply to the number of times he is successful on his next five requests.b. If he asks the same woman each of
Weather A weather forecaster states, “The chance of rain is 50% on Saturday and 50% again on Sunday. So there’s a 100% chance of rain sometime over the weekend.”If whether it rains on Saturday is independent of whether it rains on Sunday, find the actual probability of rain at least once
More ESP In another experiment with Jane Doe from the previous exercise, she had to predict which of five numbers was chosen in each of three trials. Jane Doe does not actually have ESP and is just randomly guessing.Explain why this experiment satisfies the three conditions for the binomial
Bride’s choice of surname According to a study done by the Lucy Stone League and reported by ABC News 9 in February 2011, 90% of brides take the surname of their new husband. Ann notes that of her four best friends who recently married, none kept her own name. If they had been a random sample of
Babies in China The sex distribution of new babies is close to 50% each, with the percentage of males usually being just slightly higher. In China in recent years, the percentage of female births seems to have dropped, a combination of policy limiting family size, the desire of most families to
6.90 TRUE or FALSE? IQR for normal distribution For a normally distributed random variable, the IQR is larger than the length of the interval m { s.
6.91 Multiple choice: Guess answers A question has four possible answers, only one of which is correct. You randomly guess the correct response. With 20 such questions, the distribution of the number of incorrect answersa. is binomial with n = 20 and p = 0.25.b. is binomial with n = 20 and p =
5.4 Airline accident deaths Airplane safety has been improving over the years. From 2000 to 2010, the average number of global airline deaths per year was over 1000, even when excluding the nearly 3000 deaths in the United States on September 11, 2001. The number of global airline deaths declined
5.3 Counselor availability You visit your counselor’s office at 10 randomly chosen times, and he is not available at any of those times. Does this mean that the probability of your counselor being available at his office for students equals 0? Explain.
5.2 Minesweeper The objective of the game Minesweeper is to clear a field without detonating any mines or bombs.Your friend claims that his rate of completing the game successfully is 90%.a. You decide to challenge your friend. He makes 10 attempts to complete the game, but is successful in only 7
5.1 Probability Explain what is meant by the long-run relative frequency definition of probability.
Best of seven games In professional baseball, basketball, and hockey in North America, the final two teams in the playoffs play a best of seven series of games. The first team to win four games is the champion. Use simulation with the Random Numbers app on the text’s Web site to approximate the
World Series in baseball For the 68 World Series played between 1945 and 2013, 13 (19%) ended after 4 games, 12 (18%) after 5 games, 15 (22%) after 6 games, and 28(41%) needed to go all the way to 7 games.a. Find the average number of games played based on these data. (Remember from Section 6.1
Waiting time for doubles Most discrete random variables can take on a finite number of values. Let X = the number of rolls of two dice necessary until doubles (the same number on each die) first appears.The possible values for this discrete random variable(called the geometric) are 1, 2, 3, 4, 5,
Binomial probabilities Justify the px11 - p2n - x part of the binomial formula for the probability P(x) of a particular sequence with x successes, using what you learned in Section 5.2 about probabilities for intersections of independent events.
Linear transformations: Taxes and fees Assume prices for used Audi A4s available on carmax.com follow a normal distribution with mean $23,800 and standard deviation $4,380.a. Prices quoted on carmax.com are without sales tax.To account for a 6% sales tax, you multiply each price by 1.06. What is
Mean and standard deviation for a binary random variable The previous exercise gave the formula for the standard deviation of a discrete random variable X. Let’s look at a simple case. Suppose X is a binary random variable where X = 1 with probability p and X = 0 with probability 11 - p2. a. Show
6.95 Standard deviation of a discrete probability distribution The variance of a probability distribution of a random variable is a weighted average of its squared distances from the mean m. For discrete random variables, it equals s2 = 1x - m22P1x2.Multiply each possible squared deviation 1x - m22
6.94 College acceptance The National Center for Educational Statistics reported that in 2012 the ACT college placement and admission examination had a mean of 21.1 and standard deviation of 5.3. (Source: Data from nces.ed.gov/programs/digest/d12/tables/dt12_147.asp.)a. Which probability
6.93 SAT and ethnic groups Lake Wobegon Junior College admits students only if they score above 1200 on the sum of their critical reading, mathematics, and writing scores. Applicants from ethnic group A have a mean of 1500 and a standard deviation of 300 on this test, and applicants from ethnic
6.92 Multiple choice: Terrorist coincidence? On 9/11/2002, the first anniversary of the terrorist destruction of the World Trade Center in New York City, the winning three-digit New York State Lottery number came up 9-1-1. The probability of this happening wasa. 1>1000.b. 11>100022 = 0.000001.c. 1
Manufacturing tennis balls According to the rules of tennis, a tennis ball is supposed to weigh between 56.7 grams (2 ounces) and 58.5 grams (2 1>16 ounces).A machine for manufacturing tennis balls produces balls with a mean of 57.6 grams and a standard deviation of 0.3 grams when it is operating
Metric height A Dutch researcher reads that male height in the Netherlands has a normal distribution with m = 72.0 inches and s = 4.0 inches. She prefers to convert this to the metric scale 11 inch = 2.54 centimeters2.The mean and standard deviation then have the same conversion factor.a. In
Fast-food profits Mac’s fast-food restaurant finds that its daily profits have a normal distribution with mean$140 and standard deviation $80.a. Find the probability that the restaurant loses money on a given day (that is, daily profit less than 0).b. Find the probability that the restaurant
6.50 Binomial needs fixed n For the binomial distribution, the number of trials n is a fixed number. Let X denote the number of girls in a randomly selected family in Canada that has three children. Let Y denote the number of girls in a randomly selected family in Canada (that is, the number of
6.49 Movies sample Five of the 20 movies running in movie theatres this week are comedies. A selection of four movies are picked at random. Does X = the number of movies in the sample which are comedies have the binomial distribution with n = 4 and p = 0.25? Explain why or why not.
6.48 Checking guidelines In a village having more than 100 adults, eight are randomly selected in order to form a committee of residents. 40% of adults in the village are connected with agriculture.a. Verify that the guidelines have been satisfied about the relative sizes of the population and the
6.47 Poor, poor, Pirates On September 7, 2008, the Pittsburgh Pirates lost their 82nd game of the 2008 season and tied the 1933–1948 Philadelphia Phillies major sport record (baseball, football, basketball, and hockey)for most consecutive losing seasons at 16. In fact, their losing streak
6.45 Exit poll An exit poll is taken of 3000 voters in a statewide election. Let X denote the number who voted in favor of a special proposition designed to lower property taxes and raise the sales tax. Suppose that in the population, exactly 50% voted for it.a. Explain why this scenario would seem
6.44 Is the die balanced? A balanced die with six sides is rolled 60 times.a. For the binomial distribution of X = number of 6s, what is n and what is p?b. Find the mean and the standard deviation of the distribution of X. Interpret.c. If you observe x = 0, would you be skeptical that the die is
6.43 Season performance Refer to the previous exercise. Over the course of a season, this player shoots 400 free throws.a. Find the mean and standard deviation of the probability distribution of the number of free throws he makes.b. By the normal distribution approximation, within what range would
6.42 NBA shooting In the National Basketball Association, the top free throw shooters usually have probability of about 0.90 of making any given free throw.a. During a game, one such player (Dirk Nowitzki) shot 10 free throws. Let X = number of free throws made.What must you assume for X to have a
6.40 More eBay bidding For each of the following situations, explain whether the binomial distribution applies for X.a. You are bidding on four items available on eBay. You think that you will win the first bid with probability 25%and the second through fourth bids with probability 30%.Let X denote
6.39 Bidding on eBay You are bidding on four items available on eBay. You think that for each bid, you have a 25%chance of winning it, and the outcomes of the four bids are independent events. Let X denote the number of winning bids out of the four items you bid on.a. Explain why the distribution
6.38 Unfair wealth distribution sentiment According to a study published in www.gallup.com in 2015, 63% of Americans said wealth should be more evenly distributed among a larger percentage of people. For a sample of 10 Americans, let X = number of respondents who said wealth was unfairly
6.37 Symmetric binomial Construct a graph similar to that in Figure 6.1 for each of the following binomial distributions:a. n = 4 and p = 0.50.b. n = 4 and p = 0.30.c. n = 4 and p = 0.10.d. Which if any of the graphs in parts a–c are symmetric?Without actually constructing the graph, would the
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