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Introduction To Probability And Statistics 15th Edition William Mendenhall Iii , Robert Beaver , Barbara Beaver - Solutions
8.37 Grandmas using e-mail For the question about e-mail in the previous exercise, the 14 females in the GSS of age at least 80 had the responses 0, 0, 0, 0, 1, 1, 1, 2, 2, 6, 6, 7, 7, 10.a. Using the web app, software or a calculator, find the sample mean and standard deviation and the standard
8.34 Birth weights of elephants The birth weights (in kilograms)of five elephants, selected randomly, are 133, 120, 97, 106, 124 (Source: www.elephant.se).a. Using the web app, software or a calculator, verify that the 95% confidence interval for the population mean is(98.11, 133.89).b. Name two
8.33 Talk time on smartphones One feature smartphone manufacturers use in advertising is the amount of time one can talk before recharging the battery. Below are 13 values from a random sample of the talk-time (in minutes)of smartphones running on lithium-ion batteries.The summary statistics are x
8.32 Anorexia in teenage girls A study4 compared various therapies for teenage girls suffering from anorexia, an eating disorder. For each girl, weight was measured before and after a fixed period of treatment. The variable measured was the change in weight, X = weight at the end of the study minus
8.31 Using t-table Using Table B, the web app, software or a calculator, report the t-score that you multiply by the standard error to form the margin of error for aa. 95% confidence interval for a mean with 5 observations.b. 95% confidence interval for a mean with 15 observations.c. 99% confidence
8.30 Average temperature in the United States Refer to the previous exercise. For the years 1895 to 2016 (a sample of 122 observations), the mean March monthly average temperature in the United States is 41.699°F with a standard deviation of 2.948°F.a. Find the point estimate of the monthly
8.29 Average temperature in Florida According to the National Centers for Environmental Information, the mean March monthly average temperature in Florida, for the years 1895 to 2016 (a sample of 122 observations), is 64.264°F with a standard deviation of 3.109°F (Source: www.ncdc.noaa.gov).a.
8.28 Simulating confidence intervals with poor coverage Using the Explore Coverage web app, let’s check that the large-sample confidence interval for a proportion may work poorly with small samples. In the app, set p = 0.30, n = 10 and leave the confidence level at 95%. Select to draw 100 random
8.27 Simulating confidence intervals Repeat the simulation from Activity 2, but this time simulate 1000 confidence intervals (repeatedly press the Draw Sample(s)button after selecting 100 as the number of samples to generate until you get 1000 simulations) with p = 0.5 instead of p = 0.3. Do this
8.26 Exit poll with smaller sample In the previous exercise, suppose the same proportions resulted from n = 140( instead of 1400), with counts 66 and 74.a. Now does a 95% confidence interval allow you to predict the winner? Explain.b. Explain why the same proportions but with smaller samples
8.25 Exit poll predictions A national television network takes an exit poll of 1400 voters after each has cast a vote in a state gubernatorial election. Of them, 660 say they voted for the Democratic candidate and 740 say they voted for the Republican candidate.a. Treating the sample as a random
8.24 Dispute over unlocking iPhone A national survey was conducted by the Pew Research Center (www.people-press.org) between February 18-21, 2016. Among 1002 participating adults, 51% said that Apple Inc. should assist the FBI in their investigations by unlocking the iPhone used by one of the
8.23 Chicken breast In a 2014 Consumer Reports article titled, “The High Cost of Cheap Chicken,” the magazine reported that out of 316 chicken breasts bought in retail stores throughout the United States, 207 contained E. coli bacteria.a. Find and interpret a 99% confidence interval for the
8.22 Operations growth in Luxembourg According to a survey conducted by KPMG in 2016, almost 46% of the surveyed companies intend to grow their operations in Luxembourg over the next two years
8.21 Budget impact on opportunities for young Canadians A national survey of 1500 Canadian adults conducted by Abacus Data and commissioned by EY to judge reactions to the first federal budget delivered by Finance Minister Bill Morneau, revealed that 33% of the respondents said it would have a
8.20 Trusting CNN news? USA TODAY conducted a survey of 1000 likely voters in February 2016. In the survey, 134 respondents said that CNN is the TV news or commentary source they trust the most. The interval estimation at the 95% confidence level for the proportion who trust CNN the most is (0.113,
8.17 Oppose death penalty Refer to the previous exercise.Show how you can get a 95% confidence interval for the proportion of American adults who were opposed to the death penalty from the confidence interval stated in the previous exercise for the proportion in favor.(Hint: The proportion opposed
8.15 Make industry help environment? When the 2006 GSS asked subjects whether it should or should not be the government’s responsibility to impose strict laws to make industry do less damage to the environment (variable GRNLAWS), 1403 of 1497 subjects said yes.a. What assumptions are made to
8.14 Renewable energy usage in India A survey was conducted by Mercom Communications India in 2014. Out of 1700 respondents, 1479 stated that they support subsidies for solar power over other sources.a. Estimate the population proportion who supported subsidies for solar power over other sources of
8.12 Putin A Gallup poll of 2000 Russians taken between April and June 2014 (after the Olympic games in Russia and the annexation of the Crimean peninsula) showed that 83% approved of President Putin’s performance. If random sampling were used for this survey, what is the margin of error for this
8.11 Barack Obama as president To answer these questions, refer to the data in a poll conducted by Gallup.com.(Source: http://www.gallup.com/poll/113980/gallup-dailyobama-job-approval.aspx)a. Specify the population parameter, value of the sample statistic (using the chart based on a three-day
8.10 CI for loneliness Refer to the previous exercise. The margin of error for a 95% confidence interval for the population mean is 0.12. Construct that confidence interval and interpret it.
8.9 Feel lonely often? The GSS has asked “On how many days in the past seven days have you felt lonely?” At sda.berkeley.edu/GSS, enter LONELY as the variable, select Summary Statistics in the menu of table options, and click Run the Table to see the responses.a. Report the percentage making
8.8 More youth professional football In Exercise 8.4, the proportion of American adults who would not allow a young son to play competitive football was 0.31. The estimated standard deviation of this point estimate is 0.015.a. Find and interpret the margin of error for a 95% confidence interval for
8.7 Nutrient effect on growth rate Researchers are interested in the effect of a certain nutrient on the growth rate of plant seedlings. Using a hydroponics growth procedure that used water containing the nutrient, they planted six tomato plants and recorded the heights of each plant 14 days after
8.6 Game apps The Google Play app store for smartphones offers hundreds of games to download for free or for a small fee. The ones for which a fee is charged are called paid games. For a random sample of five paid games taken in July 2014 on the Google platform, the following fees were charged:
8.5 Government spying In 2014, news reports worldwide alleged that the U.S. government had hacked German chancellor Angela Merkel’s cell phone. A Pew Research Center survey of German citizens at about that time asked whether they find it acceptable or unacceptable for the U.S. government to
8.4 Youth professional football In a survey of 1009 American adults in 2016, 313 said they would not allow a young son to play competitive football (www.forbes.com). Find the point estimate of the population proportion of these respondents.
8.3 Projecting winning candidate News coverage during a recent election projected that a certain candidate would receive 54.8% of all votes cast; the projection had a margin of error of {3%.a. Give a point estimate for the proportion of all votes the candidate will receive.b. Give an interval
8.2 Video on demand A recent study from Nielsen (available from nielsen.com; search for “The Cross-Platform Report”) took a sample to investigate how video on demand and other subscription-based services (such as Netflix, Amazon Prime, and Hulu) change TV viewing behavior of U.S. adults. Among
8.1 Health care A study dealing with health care issues plans to take a sample survey of 1500 Americans to estimate the proportion who have health insurance and the mean dollar amount that Americans spent on health care this past year.a. Identify two population parameters that this study will
7.65 Sample versus sampling Each student should bring 10 coins to class. For each coin, observe its age, the difference between the current year and the year on the coin.a. Using all the students’ observations, the class should construct a histogram of the sample ages. What is its shape?b. Now
7.64 Coin-tossing distributions For a single toss of a balanced coin, let x = 1 for a head and x = 0 for a tail.a. Construct the probability distribution for x and calculate its mean. (You can think of this as the population distribution corresponding to a very long sequence of tosses.)b. The coin
7.60 Sample population Let X = GPA for students in your school.a. What would the sampling distribution of the sample mean look like if you sampled every student in the school, so the sample size equals the population size?(Hint: The sample mean then equals the population mean.)b. How does the
7.59 Multiple choice: Sampling distribution The sampling distribution of a sample mean for a random sample size of 100 describesa. How sample means tend to vary from random sample to random sample of size 100.b. How observations tend to vary from person to person in a random sample of size 100.c.
7.58 Multiple choice: Sampling distribution of sample proportion In a class of 150 students, the professor has each person toss a fair coin 50 times and calculate the proportion of times the tosses come up heads. Roughly 95% of students should have proportions between which two numbers?a. 0.49 and
7.57 Multiple choice: CLT The central limit theorem impliesa. All variables have approximately bell-shaped data distributions if a random sample contains at least about 30 observations.b. Population distributions are normal whenever the population size is large.c. For sufficiently large random
7.56 Multiple choice: Standard deviation Which of the following is not correct? The standard deviation of a statistic describesa. The standard deviation of the sampling distribution of that statistic.b. The standard deviation of the sample data measurements.c. How close that statistic falls to the
7.55 True or false As the sample size increases, the standard deviation of the sampling distribution of x increases.Explain your answer.
7.54 Winning at roulette Part b of Example 7 used the central limit theorem to approximate the probability of coming out ahead if you bet $10 on red on each of 40 roulette wheel spins. For each spin, the winnings are$10 with probability 18/38 and - $10 with probability 20/38. You are interested in
7.53 Simulating pizza preference with p = 0.6 Access the Sampling Distribution of the Sample Proportion web app.When p = 0.6 and the sample size n = 3, the mean and standard deviation of the sampling distribution (given in the table in part a of Exercise 7.51) are equal to 0.6 and 0.283. With the
7.50 Sampling distribution via the binomial Refer to the previous exercise, in which the proportion of people preferring pizza A is p = 0.5 and a sample of size n = 3 is taken. The sampling distribution of the sample proportion of people preferring pizza A as shown in part b of that exercise can
7.48 Purpose of sampling distribution You’d like to estimate the proportion of all students in your school who are fluent in more than one language. You poll a random sample of 50 students and get a sample proportion of 0.12. Explain why the standard deviation of the sampling distribution of the
7.47 What good is a standard deviation? Explain how the standard deviation of the sampling distribution of a sample proportion gives you useful information to help gauge how close a sample proportion falls to the unknown population proportion.
7.46 What is a sampling distribution? How would you explain to someone who has never studied statistics what a sampling distribution is? Explain by using the example of polls of 1000 Canadians for estimating the proportion who think the prime minister is doing a good job.
7.45 CLT for custom population Access the Sampling Distribution for a Sample Mean web app and select Build Own as the shape for the population distribution. By typing numbers into the text field, you can create your own population distribution. Repeating a number several times will make the
7.44 Too little or too much cola? Refer to the previous exercise. When a machine for dispensing a cola drink into bottles is in statistical control, the amount dispensed has a mean of 500 ml (milliliters) and a standard deviation of 4 ml.a. In constructing a control chart to monitor this process
7.42 Number of pets According to data on StatCrunch.com, the mean number of X = pets owned per household in a certain area in the United States was 1.88 pets, and the standard deviation was 1.67.a. Does X have a normal distribution? Explain.b. For a random sample of 100 houses, describe the
7.41 PDI The scores on the Psychomotor Development Index (PDI), a scale of infant development, have a normal population distribution with mean 100 and standard deviation 15. An infant is selected at random.a. Find the z-score for a PDI value of 90.b. A study uses a random sample of 225 infants.
7.40 Bank machine withdrawals An executive in an Australian savings bank decides to estimate the mean amount of money withdrawn in bank machine transactions. From past experience, she believes that $50 (Australian) is a reasonable guess for the standard deviation of the distribution of withdrawals.
7.39 Student debt In 2005, a study was conducted in West Texas A&M University. It showed that the average student debt in the United States was $18,367 with a standard deviation of $4709. (Source: http://swer.wtamu.edu/sites/default/files/Data/15-26-49-178-1-PB.pdf.)a. Suppose 100 students had been
7.38 Home runs Based on data from the 2010 Major League Baseball season, X = number of home runs the San Francisco Giants hit in a game has a mean of 1.0 and a standard deviation of 1.0.a. Do you think X has a normal distribution? Why or why not?b. Suppose that this year X has the same
7.37 Aunt Erma’s restaurant In Aunt Erma’s Restaurant, the daily sales follow a probability distribution that has a mean of m = $900 and a standard deviation of s = $300. This past week the daily sales for the seven days had a mean of $980 and a standard deviation of $276. Consider these seven
7.36 Returning shipment Refer to the previous exercise, in which the manufacturer will return the entire shipment if more than 5% defective chips are found in the sample.a. Find the probability that the shipment will be returned if the manufacturer decides to test only 380 randomly selected chips
7.35 Defective chips A supplier of electronic chips for tablets claims that only 4% of his chips are defective. A manufacturer tests 500 randomly selected chips from a large shipment from the supplier for potential defects.a. Find the mean and standard deviation for the distribution of the sample
7.34 Basketball shooting In college basketball, a shot made from beyond a designated arc radiating about 20 feet from the basket is worth three points instead of the usual two points given for shots made inside that arc. Over his career, University of Florida basketball player Lee Humphrey made 45%
7.33 Alzheimer’s According to the Alzheimer’s Association,2 as of 2014 Alzheimer’s disease affects 1 in 9 Americans over the age of 65. A study is planned of health problems the elderly face. For a random sample of Americans over the age of 65, report the shape, mean, and standard deviation
7.32 Cardiovascular diseases According to The American Heart Association in 2011, about 1 in every 3 deaths in the U.S. was from cardiovascular diseases. (Source: Data from www.heart.org, December 17, 2014.)a. For a random sample of 100 deaths in America in 2011, find the mean and standard
7.31 Exam performance An exam consists of 50 multiplechoice questions. Based on how much you studied, for any given question you think you have a probability of p = 0.70 of getting the correct answer. Consider the sampling distribution of the sample proportion of the 50 questions on which you get
7.30 Sampling distribution for normal population Access the Sampling Distribution of the Sample Mean web app and select Bell-Shaped for the shape of the population distribution, which looks similar to the fourth column in Figure 7.11. Select a value for the population mean and standard deviation.
7.29 CLT for skewed population Access the Sampling Distribution of the Sample Mean web app and position the slider for the skewness of the default population distribution to the smallest value. The population distribution now looks similar to the one in the third column of Figure 7.11. Repeat parts
7.28 Central limit theorem for uniform population Let’s use the Sampling Distribution of the Sample Mean web app accessible from the book’s website to show that the first population distribution shown in Figure 7.11 has a more nearly normal sampling distribution for the mean as n increases.
7.27 Average time to fill job positions For all job positions in a company, assume that, a few years ago, the average time to fill a job position was 37 days with a standard deviation of 12 days. For the purpose of comparison, the manager of the hiring department selected a random sample of 100 of
7.26 Average price of an ebook According to the website http://www.digitalbookworld.com, the average price of a bestselling ebook increased to $8.05 in the week of February 18, 2015 from $6.89 in the previous week.Assume the standard deviation of the price of a bestselling ebook is $1 and suppose
7.25 Blood pressure Vincenzo Baranello was diagnosed with high blood pressure. He was able to keep his blood pressure in control for several months by taking blood pressure medicine (amlodipine besylate). Baranello’s blood pressure is monitored by taking three readings a day, in early morning, at
7.24 Survey accuracy According to the U.S. Census Bureau, Current Population Survey, Annual Social and Economic Supplement, the average income for females was $28,466 and the standard deviation was $36,961 in 2015. A sample of 1,000 females was randomly chosen from the entire United States
7.23 Restaurant profit? Jan’s All You Can Eat Restaurant charges $8.95 per customer to eat at the restaurant.Restaurant management finds that its expense per customer, based on how much the customer eats and the expense of labor, has a distribution that is skewed to the right with a mean of $8.20
7.22 Dropped from plan The previous exercise mentions that the duration of your phone calls follows a distribution with mean m = 2.8 minutes and standard deviation s = 2.1 minutes. From a random sample of n = 45 calls, your parents computed a sample mean of x = 3.4 minutes and a sample standard
7.21 Shared family phone plan A recent personalized information sheet from your wireless phone carrier claims that the mean duration of all your phone calls was m = 2.8 minutes with a standard deviation of s = 2.1 minutes.a. Is the population distribution of the duration of your phone calls likely
7.20 Canada lottery In one lottery option in Canada (Source:Lottery Canada), you bet on a six-digit number between 000000 and 999999. For a $1 bet, you win $100,000 if you are correct. The mean and standard deviation of the probability distribution for the lottery winnings are m = 0.10(that is, 10
7.19 Simulate rolling dice Access the Sampling Distribution of the Sample Mean (discrete variable) web app on the book’s website. Enter the probabilities P1X = x2 of 0.1667 for the numbers 1 through 6 to specify the probability distribution of a fair die. (This is a discrete version of the
7.18 Performance of airlines In 2015, the on-time arrival rate of all major domestic and regional airlines operating between Australian airports has a bell-shaped distribution roughly with mean 0.86 and standard deviation 0.1.a. Let X denote the number of flights arriving on time when you observe
7.17 Rolling one die Let X denote the outcome of rolling a die.a. Construct a graph of the (i) probability distribution of X and (ii) sampling distribution of the sample mean for n = 2. (You can think of (i) as the population distribution you would get if you could roll the die an infinite number
7.16 Education of the self-employed According to a recent Current Population Reports, the population distribution of number of years of education for self-employed individuals in the United States has a mean of 13.6 and a standard deviation of 3.0.a. Identify the random variable X whose population
7.15 Simulate taking midterms Assume that the distribution of the score on a recent midterm is bell shaped with population mean m = 70 and population standard deviation s = 10. You randomly sample n = 12 students who took the midterm. Using the Sampling Distribution of the Sample Mean web app
7.14 Beauty contest election A finalist of a Miss University contest believes that 52% of Facebook voters will vote for her. However, she is worried about low voter turnout.a. Assuming she truly has the support of 52% of all Facebook voters, find the mean and standard deviation of the sampling
7.13 Shapes of distributionsa. With random sampling, does the shape of the data distribution tend to resemble more closely the sampling distribution or the population distribution?Explain.b. Is the sampling distribution of the sample proportion always bell shaped? Investigate with the Sampling
7.12 Gender distributions At a university, 60% of the 7,400 students are female. The student newspaper reports results of a survey of a random sample of 50 students about various topics involving alcohol abuse, such as participation in binge drinking. They report that their sample contained 26
7.11 Syracuse full-time students You’d like to estimate the proportion of the 14,201 undergraduate students at Syracuse University who are full-time students. You poll a random sample of 350 students, of whom 330 are full-time.Unknown to you, the proportion of all undergraduate students who are
7.9 Buying a car A car dealer offers a $500 discount to customers if they agree to buy a car immediately without doing further research. Suppose 30% of all customers who visit him accept this offer. Depending on whether or not a given customer accepts the offer, let X be either 1 or 0,
7.8 Awareness about cancer An experiment consists of asking your friends if they would like to raise money for a cancer association. Assuming half of your friends would agree to raise money, construct the sampling distribution of the sample proportion of affirmative answers obtained for a sample
7.7 Random variability in baseball A baseball player in the major leagues who plays regularly will have about 500 at-bats (that is, about 500 times he can be the hitter in a game) during a season. Suppose a player has a 0.300 probability of getting a hit in an at-bat. His batting average at the end
7.6 Exit poll and n Refer to the previous exercise.a. In partb, if the sampling distribution of the sample proportion had mean 0.409 and the standard deviation 0.008, give an interval of values within which the sample proportion will almost certainly fall. (Hint: You can use the approximate
7.5 Other scenario for exit poll Refer to Examples 1 and 2 about the exit poll, for which the sample size was 3889. In that election, 40.9% voted for Whitman.a. Define a binary random variable X taking values 0 and 1 that represents the vote for a particular voter(1 = vote for Whitman and 0 =
7.4 iPhone apps Let p = 0.25 be the proportion of iPhone owners who have a given app. For a particular iPhone owner, let x = 1 if they have the app and x = 0 otherwise.For a random sample of 50 owners:a. State the population distribution (that is, the probability distribution of X for each
7.3 House owners in a district In order to estimate the proportion p of people who own houses in a district, we choose a random sample from the population and study its sampling distribution. Assuming p = 0.3, use the appropriate formulas from this section to find the mean and the standard
7.2 Simulate condo solicitations A company that is selling condos in Florida plans to send out an advertisement for the condos to 500 potential customers, in which they promise a free weekend at a resort on the Florida coast in exchange for agreeing to attend a four-hour sales presentation.The
7.1 Simulating the exit poll Simulate an exit poll of 100 voters, using the Sampling Distribution web app accessible from the book’s website, assuming that the population proportion is 0.53. Refer to Activity 1 for guidance on using the app.a. Simulate drawing one random sample of size 100.What
5. Use the results of part 3 to evaluate the probability that the largest evening’s winnings were as great as $1160. The technique of simulating a process that contains random elements and repeating the process over and over to see how it behaves is called a Monte Carlo procedure. It is widely
4. Use the results of part 2 to evaluate the probability of 7 out of 365 evenings resulting in a loss of the total $1000 stake. The technique of simulating a process that contains random elements and repeating the process over and over to see how it behaves is called a Monte Carlo procedure. It is
3. Find the expected value and variance for the evening’s gain, the sum of the gains or losses for the 200 bets of $5 each. How does this compare with Seligman’s simulated average loss of $55 per day? The technique of simulating a process that contains random elements and repeating the process
2. Find the expected value and variance of the gain x from part 1. The technique of simulating a process that contains random elements and repeating the process over and over to see how it behaves is called a Monte Carlo procedure. It is widely used in business and economics to investigate the
1. To evaluate the results of Seligman’s Monte Carlo experiment, first find the probability distribution of the gain x on a single $5 bet. The technique of simulating a process that contains random elements and repeating the process over and over to see how it behaves is called a Monte Carlo
22. Filling Soda Cans A bottler of soft drinks packages cans in six-packs. Suppose that the fill per can has an approximate normal distribution with a mean of 12 fluid ounces and a standard deviation of 0.2 fluid ounces.a. What is the distribution of the total fill for a case of 24 cans?b. What is
21. Elevator Loads The maximum load (with a generous safety factor) for the elevator in an office building is 910 kilograms. The relative frequency distribution of the weights of all men and women using the elevator is mound-shaped (slightly skewed to the heavy weights), with mean m equal to 68
20. Hard Hats The safety requirements for hard hats worn by construction workers and others specify that each of three hats pass the following test. A hat is mounted on an aluminum head form. A 3.5-kilogram steel ball is dropped on the hat from a height of 1.5 meters, and the resulting force is
19. Refer to Exercise 18.a. Use the data entry method in your calculator to find the mean and standard deviation of the 50 values of x given in Exercise 18, part c.b. Compare the values calculated in part a to the theoretical mean m and the theoretical standard deviation s / n for the sampling
17. Polling College Students In conducting polls of college students, it is increasingly difficult to get a random sample of college students in which every college student has the same chance of being included in the sample. Consider the following scenario used by the Gallup organization24 to
16. Strawberries An experimenter wants to find an appropriate temperature at which to store fresh strawberries to minimize the loss of ascorbic acid. There are 20 storage containers, each with controllable temperature, in which strawberries can be stored. If two storage temperatures are to be used,
15. Lightbulbs, again Refer to Exercise 13. During a given week the number of defective bulbs in each of five samples of 100 were found to be 2, 4, 9, 7, and 11.Is there reason to believe that the production process has been producing an excessive proportion of defectives at any time during the
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