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elementary statistics
Just The Essentials Of Elementary Statistics 10th Edition Robert Johnson, Patricia Kuby - Solutions
Construct the confidence interval for Exercise 12 assuming that s is known to be 2.55 chocolate chips.
Construct the confidence interval for Exercise 11 assuming that s is known to be 7718.8 thousand dollars.
Construct the confidence interval for Exercise 10 assuming that s is known to be 0.366 ppm.
Construct the confidence interval for Exercise 9 assuming that s is known to be 5.013 km.
Second-Hand Smoke Figure 6 from Example 5 shows a graph of three different confidence intervals. Use the cotinine levels of smokers listed in Data Set 9 from Appendix: Data Sets and construct the 95% confidence interval estimate of the population mean m.
Earthquake Magnitudes Use the earthquake magnitudes listed in Data Set 16 from Appendix: Data Sets and construct a 99% confidence interval estimate of the mean of all such magnitudes.
Sample Size Using Sample Data Refer to Data Set 16 in Appendix: Data Sets and find the maximum and minimum earthquake magnitudes, then use those values with the range rule of thumb to estimate s. How many earthquakes must you randomly select if you want to be 95% confident that the sample mean
Sample Size Using Sample Data Refer to Data Set 1 in Appendix: Data Sets and find the maximum and minimum pulse rates for males, then use those values with the range rule of thumb to estimate s. How many adult males must you randomly select and test if you want to be 95% confident that the sample
Sample Size Using Range Rule of Thumb You want to estimate the mean amount of annual tuition being paid by current full-time college students in the United States.First use the range rule of thumb to make a rough estimate of the standard deviation of the amounts spent. It is reasonable to assume
Sample Size Using Range Rule of Thumb You want to estimate the mean SAT score of all college applicants. First use the range rule of thumb to make a rough estimate of the standard deviation of those scores. Possible SAT scores range from 600 to 2400. Use the estimated standard deviation to
Facebook Time You want to estimate the mean amount of time Internet users spend on Facebook each month. How many Internet users must be surveyed in order to be 95% confident that your sample mean is within 15 minutes of the population mean? Based on results from a prior Nielsen survey, assume that
Buying a Corvette Research of selling prices for used two-year-old Corvettes reveals that they have a standard deviation of $2157 (based on data from Edmunds.com). How many selling prices must you obtain in order to estimate the mean selling price of these cars? Assume that you want 98% confidence
Mean Grade Point Average As part of a study of grade inflation, you want to estimate the mean grade point average of all current college students in the United States. All grade point averages are to be standardized for a scale between 0 and 4.How many grade point averages must be obtained so that
The standard deviation for this population is probably less than 15 because it is a group with less variation than a group randomly selected from the general population; therefore, if we use s = 15 we are being conservative by using a value that will make the sample size at least as large as
Mean IQ of Professional Pilots The Wechsler IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of professional pilots. We want to be 90% confident that our sample mean is
Brain Volume Listed below are brain volumes (cm3) of unrelated subjects used in a study. (See Data Set 6 in Appendix: Data Sets.) Use the sample data to construct a 99%confidence interval estimate of the mean of the brain volume of the population. Given that typical brain volumes are between 950
Use the sample data to construct a 95% confidence interval estimate of the mean of the lead concentrations for the population of all such medicines.If a safety standard requires lead concentrations less than 7 mg/g, does it appear that the population mean is less than that level?3.0 6.5 6.0 5.5
Lead in Medicine Listed below are the lead concentrations (in mg/g) measured in different Ayurveda medicines. Ayurveda is a traditional medical system commonly used in India.The lead concentrations listed here are from medicines manufactured in the United States.The data are based on the article
Ages of Race Car Drivers Listed below are the ages (years) of randomly selected race car drivers (based on data reported in USA Today). Construct a 98% confidence interval estimate of the mean age of all race car drivers.32 32 33 33 41 29 38 32 33 23 27 45 52 29 25
Cell Phone Radiation Listed below are the measured radiation emissions (in W/kg)corresponding to these cell phones: Samsung SGH-tss9, Blackberry Storm, Blackberry Curve, Motorola Moto, T-Mobile Sidekick, Sanyo Katana Eclipse, Palm Pre, Sony Ericsson, Nokia 6085, Apple iPhone 3G S, Kyocero Neo
Years in College Listed below are the numbers of years it took for a random sample of college students to earn bachelor’s degrees (based on data from the National Center for Education Statistics). Construct a 90% confidence interval estimate of the mean time required for all college students to
Harry Potter Listed below are the gross amounts (in millions of dollars) earned from box office receipts for the movie Harry Potter and the Half-Blood Prince. The movie opened on a Wednesday, and the amounts are listed in order for the first 14 days of the movie’s release. Use the sample values
Insomnia Treatment A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomnia in older subjects. Before treatment with zopiclone, 16 subjects had a mean wake time of 102.8 min. After treatment with zoplicone, the 16 subjects had a mean wake time of 98.9 min
Garlic for Reducing Cholesterol In a test of the effectiveness of garlic for lowering cholesterol, 49 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes (before minus after) in their levels of LDL cholesterol(in mg/dL) had a mean of
Atkins Weight Loss Program In a test of weight loss programs, 40 adults used the Atkins weight loss program. After 12 months, their mean weight loss was found to be 2.1 lb, with a standard deviation of 4.8 lb. Construct a 90% confidence interval estimate of the mean weight loss for all such
Mean Body Temperature Data Set 3 in Appendix: Data Sets includes a sample of 106 body temperatures having a mean of 98.20oF and a standard deviation of 0.62oF. Construct a 95% confidence interval estimate of the mean body temperature for the entire population.What does the result suggest about the
Chocolate Chip Cookies Suppose the mean of the numbers of chocolate chips in a sample of 40 Chips Ahoy regular cookies is 23.95 chocolate chips and the standard deviation is 2.55 chocolate chips. Construct a 99% confidence interval estimate of the mean number of chocolate chips in all such cookies.
CEO Compensation Listed below are the recent annual compensation amounts (in thousands of dollars) for a random sample of chief executive officers (Mulally from Ford, Jobs from Apple, Kent from Coca-Cola, Otellini from Intel, and McNerney from Boeing). The mean of the sample is 12,898 (thousand
Mercury in Sushi Listed below are the amounts of mercury (in parts per million, or ppm) found in tuna sushi sampled at different stores in New York City. The study was sponsored by the New York Times, and the stores (in order) are D’Agostino, Eli’s Manhattan, Fairway, Food Emporium, Gourmet
Earthquake Depths Data Set 16 in Appendix: Data Sets lists the depths (km) of a sample of 50 earthquakes. Those 50 depths have a mean of 9.808 km and a standard deviation of 5.013 km. Construct a 98% confidence interval estimate of the mean of all such depths. Is the confidence interval affected by
Confidence level is 99%, s is known to be $4,385,000, and the dotplot of 40 sample values of professional baseball players is as shown in Exercise 7.Confidence Intervals. In Exercises 9–24, construct the confidence interval.
Interpreting a Confidence Interval The results in the screen display are based on a 95% confidence level. Write a statement that correctly interprets the confidence interval.
Degrees of Freedom For the accompanying screen display, a simple random sample of size n = 40 was obtained from the population of duration times (seconds) of eruptions of the Old Faithful geyser.a. What is the number of degrees of freedom that should be used for finding the critical value ta>2?b.
Confidence Interval Refer to the accompanying screen display.a. Express the confidence interval in the format that uses the “less than” symbol.b. Identify the best point estimate of m and the margin of error.
One-Sided Confidence Interval A one-sided claim about a population proportion is a claim that the proportion is less than (or greater than) some specific value. Such a claim can be formally addressed using a one-sided confidence interval for p, which can be expressed as p 6 pn + E or p 7 pn - E,
Coping with No Success According to the Rule of Three, when we have a sample size n with x = 0 successes, we have 95% confidence that the true population proportion has an upper bound of 3>n. (See “A Look at the Rule of Three,” by Jovanovic and Levy, American Statistician, Vol. 51, No. 2.)a. If
Interpreting Confidence Interval Limits Repeat Exercise 38 using a 99% confidence level. What is unusual about the result? Does common sense suggest a modification of the result?
Confidence Interval from Small Sample Special tables are available for finding confidence intervals for proportions involving small numbers of cases, where the normal distribution approximation cannot be used. For example, given x = 3 successes among n = 8 trials, the 95% confidence interval found
Arrival Delays Refer to Data Set 15 in the Appendix: Data Sets. A flight is considered on time if it arrives no later than 15 minutes after the scheduled arrival time. The last column of Data Set 15 lists arrival delays, so on-time flights correspond to values in that column that are 15 or less.
Heights of Presidents Refer to Data Set 12 in the Appendix: Data Sets. Treat the data as a sample and find the proportion of presidents who were taller than their opponents.Use that result to construct a 95% confidence interval estimate of the population percentage.Based on the result, does it
On-time Rate You have been given the task of estimating the percentage of Southwest flights that arrive on time, which is no later than 15 minutes after the scheduled arrival time.How many flights must you survey in order to be 80% confident that your estimate is within three percentage points of
Twitter As manager for an advertising company, you must plan a campaign designed to increase Twitter usage. You want to first determine the percentage of adults who know what Twitter is. How many adults must you survey in order to be 90% confident that your estimate is within five percentage points
Windows Penetration You plan to develop a new software system that you believe will surpass the success of Google and Facebook combined. In planning for the operating system that you will use, you need to estimate the percentage of computers that use Windows. How many computers must be surveyed in
Airline Seating You are the operations manager for American Airlines and you are considering a higher fare level for passengers in aisle seats. You want to estimate the percentage of passengers who now prefer aisle seats. How many randomly selected air passengers must you survey? Assume that you
Robberies Find the sample size needed to estimate the percentage of robberies in Texas that result in arrests. Use a 0.04 margin of error, use a confidence level of 80%, and assume that pn and qn are unknown.
Medication Usage In a survey of 3005 adults aged 57 through 85 years, it was found that 81.7% of them used at least one prescription medication (based on data from “Use of Prescription and Over-the-Counter Medications and Dietary Supplements Among Older Adults in the United States,” by Qato et
Cell Phones and Cancer A study of 420,095 Danish cell phone users found that 0.0321% of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such cancer was found to be 0.0340% for those not using cell phones.The data are from the Journal of the
Misleading Survey Responses In a survey of 1002 people, 70% said that they voted in a recent presidential election (based on data from ICR Research Group). Voting records show that 61% of eligible voters actually did vote.a. Find a 98% confidence interval estimate of the proportion of people who
M&Ms The Mars candy company claims that 13% of its M&M candies are brown, but Data Set 20 in the Appendix: Data Sets a data set lists data from 100 M&Ms, and 8% of them are brown. Use the sample data to construct a 98% confidence interval estimate of the proportion of brown M&Ms. Does it appear
Job Interviews In a Harris poll of 514 human resource professionals, 90% said that the appearance of a job applicant is most important for a good first impression.a. Among the 514 human resource professionals who were surveyed, how many of them said that the appearance of a job applicant is most
Job Interviews In a Harris poll of 514 human resource professionals, 45.9% said that body piercings and tattoos were big grooming red flags.a. Among the 514 human resource professionals who were surveyed, how many of them said that body piercings and tattoos were big grooming red flags?b. Construct
Want Boss’s Job? In a USA Today survey, 20.8% of 144 respondents said that they aspired to have their boss’s job. Construct a 95% confidence interval estimate of the percentage of all workers who aspire to have their boss’s job. How are the results affected by the additional knowledge that
Online Books A Consumer Reports Research Center survey of 427 women showed that 29.0% of them purchase books online.a. Among the 427 women who were surveyed, what is the number of women who said that they purchase books online?b. Find a 95% confidence interval estimate of the percentage of all
Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas.a. Find a 95% confidence interval estimate of the percentage of yellow peas.b. Based on his theory of genetics, Mendel expected that 25% of the
Touch Therapy When she was 9 years of age, Emily Rosa did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field.She flipped a coin to select either her right hand or her left hand, then she asked the therapists to identify the
Gender Selection The Genetics & IVF Institute conducted a clinical trial of the YSORT method designed to increase the probability of conceiving a boy. As of this writing, 291 babies were born to parents using the YSORT method, and 239 of them were boys.a. What is the best point estimate of the
Gender Selection The Genetics & IVF Institute conducted a clinical trial of the XSORT method designed to increase the probability of conceiving a girl. As of this writing, 945 babies were born to parents using the XSORT method, and 879 of them were girls.a. What is the best point estimate of the
From an Angus Reid Public Opinion poll in which respondents were asked if they felt that U.S. nuclear weapons made them feel safer: n = 1005, x = 543 who said “yes.” Use a confidence level of 80%.
From a Prince Market Research poll in which respondents were asked if they acted to annoy a bad driver: n = 2518, x = 1083 who said that they honked. Use a 90% confidence level.
From a 3M Privacy Filters poll in which respondents were asked to identify their favorite seat when they fly: n = 806, x = 492 who chose the window seat. Use a 99% confidence level.
From a KRC Research poll in which respondents were asked if they felt vulnerable to identity theft: n = 1002, x = 531 who said “yes.” Use a 95% confidence level.
Express the confidence interval 0.270 { 0.087 in the form of pn - E 6 p 6 pn + E.
Express the confidence interval (0.0268, 0.133) in the form of pn - E 6 p 6 pn + E.
Express the confidence interval 0.165 6 p 6 0.335 in the form of pn { E.
Express the confidence interval 0.0641 6 p 6 0.186 in the form of pn { E.
Find za>2 for a = 0.04.
Find za>2 for a = 0.10.
Find the critical value za>2 that corresponds to a 99% confidence level.
Find the critical value za>2 that corresponds to a confidence level of 80%.
Confidence Levels Given specific sample data, such as the data given in Exercise 1, which confidence interval is wider: the 95% confidence interval or the 80% confidence interval? Why is it wider?Finding Critical Values. In Exercises 5–8, find the indicated critical z value.
Notation For the poll described in Exercise 1, what do pn, qn, n, E, and p represent? If the confidence level is 95%, what is the value of a?
Margin of Error For the poll described in Exercise 1, describe what is meant by the statement that “the margin of error is {3 percentage points.”
Poll Results in the Media USA Today provided a “snapshot” illustrating poll results from 1910 professionals who interview job applicants. The illustration showed that 26% of them said the biggest interview turnoff is that the applicant did not make an effort to learn about the job or the
Student A and Student B were discussing one entry in a probability distribution chart:x P(x)2 0.1 Student B thought this entry was okay because P(x) was a value between 0.0 and 1.0.Student A argued that this entry was impossible for a probability distribution because x was 2 and negatives are not
Student A uses a relative frequency distribution for a set of sample data and calculates the mean and standard deviation using formulas from Chapter 5. Student A justifies her choice of formulas by saying that since relative frequencies are empirical probabilities, her sample is represented by a
What properties must an experiment possess in order for it to be a binomial probability experiment?
A T-shirt manufacturing company advertises that the probability of an individual T-shirt being irregular is 0.1. A box of 12 such Tshirts is randomly selected and inspected.a. What is the probability that exactly 2 of these 12 T-shirts are irregular?b. What is the probability that exactly 9 of
Design your own study of caffeine drinking.a. Define a specific population that you will sample, describe your sampling plan, and collect your data.b. Express your sample as a relative frequency distribution and draw a histogram.c. Express your sample as a frequency distribution and find the sample
a. What variable could be used to describe all five of the events shown in the“Americans like their coffee!” graphic(p. 269)?b. Is the variable in part a discrete or continuous?Why?c. Are events x 0, 1, 2, . . . mutually exclusive?Explain why or why not.d. What characteristics of a circle
A business firm is considering two investments.It will choose the one that promises the greater payoff. Which of the investments should it accept? (Let the mean profit measure the payoff.)Invest in Tool Shop Invest in Book Store Profit Probability Profit Probability$100,000 0.10 $400,000 0.20
In another germination experiment involving old seed, 50 rows of seeds were planted. The number of seeds germinating in each row were recorded in the following table (each row contained the same number of seeds).Number Germinating Number of Rows Number Germinating Number of Rows 0 17 3 2 1 20 4 1 2
The state bridge design engineer has devised a plan to repair North Carolina’s 4706 bridges that are currently listed as being in either poor or fair condition. The state has a total of 13,268 bridges.Before the governor will include the cost of this plan in his budget, he has decided to
Imagine that you are in the midst of purchasing a lottery ticket and the person behind the counter prints too many tickets with your numbers.What would you do? The results of an online survey were as follows:Let them keep the tickets? 30.77%Trust the person to delete them? 15.38%Buy the extra ones
R&B/hip-hop songs accounted for more than 60% of radio’s top 100 hits in 2004, according to data from Nielsen BDS and Arbitron as reported in USA Today on January 5, 2005. A new radio station, appropriately named Fickle, plays all types of music from the list of the top 100 hits including
Of those seeking a driver’s license, 70% admitted that they would not report someone if he or she copied some answers during the written exam.You have just entered the room and see 10 people waiting to take the written exam. What is the probability that if the incident happened, 5 of the 10 would
a. Explain the difference and the relationship between a probability distribution and a probability function.b. Explain the difference and the relationship between a probability distribution and a frequency distribution, and explain how they relate to a population and a sample.
What are the two basic properties of every probability distribution?
Did you ever buy an incandescent light bulb that failed (either burned out or did not work) the first time you turned the switch on? When you put a new bulb into a light fixture, you expect it to light, and most of the time it does. Consider 8-packs of 60-watt bulbs and let x be the number of bulbs
Imprints Galore buys T-shirts (to be imprinted with an item of the customer’s choice) from a manufacturer who guarantees that the shirts have been inspected and that no more than 1% are imperfect in any way. The shirts arrive in boxes of 12. Let x be the number of imperfect shirts found in any
A binomial random variable x is based on 15 trials with the probability of success equal to 0.2.Find the probability that this variable will take on a value more than 2 standard deviations from the mean.
A binomial random variable x is based on 15 trials with the probability of success equal to 0.4. Find the probability that this variable will take on a value more than 2 standard deviations above the mean.
The probability of success on a single trial of a binomial experiment is known to be 14. The random variable x, number of successes, has a mean value of 80. Find the number of trials involved in this experiment and the standard deviation of x.
A binomial random variable has a mean equal to 200 and a standard deviation of 10. Find the values of n and p.
According to the American Payroll Association(September 10, 2004), when asked, “Do you support the use of biometric technology (fingerprints or hand recognition) to record employee time and attendance?” the majority of workers say they wouldn’t mind. However, 28% object to it, believing it is
According to United Mileage Plus Visa (November 22, 2004), 41% of passengers say they“put on the earphones” to avoid being bothered by their seat mates during flights. To show how important, or not important, the earphones are to people, consider the variable x to be the number of people in a
Find the mean and standard deviation for each of the following binomial random variables in parts a–c:a. The number of sixes seen in 50 rolls of a dieb. The number of defective televisions in a shipment of 125 (The manufacturer claimed that 98% of the sets were operative.)c. The number of
Find the mean and standard deviation of x for each of the following binomial random variables:a. The number of tails seen in 50 tosses of a quarterb. The number of left-handed students in a classroom of 40 students (assume that 11% of the population is left-handed)c. The number of cars found to
Consider the binomial distribution where n 11 and p 0.05 (see Exercise 5.86).a. Use the distribution [Exercise 5.86(b) or Table 2] and find the mean and standard deviation using formulas (5.1), (5.3a), and (5.4).b. Compare the results of part a with the answers found in Exercise 5.86(a).
Consider the binomial distribution where n 11 and p 0.05.a. Find the mean and standard deviation using formulas (5.7) and (5.8).b. Using Table 2 in Appendix B, list the probability distribution and draw a histogram.c. Locate and on the histogram.
Find the mean and standard deviation for the binomial random variable x with n 30 and p 0.6, using formulas (5.7) and (5.8).
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