Determine each of the following areas under the standard normal (z) curve: a. To the left of -1.28 b. To the right of 1.28 c. Between -1 and 2 d. To the right of 0 e. To the right of -5 f. Between -1.6 and 2.5 g. To the left of 0.23
> The distribution of the number of items produced by an assembly line during an 8-hour shift can be approximated by a normal distribution with mean value 150 and standard deviation 10. a. What is the approximate probability that the number of items produc
> Suppose that 65% of all registered voters in a certain area favor a seven-day waiting period before purchase of a handgun. Among 225 randomly selected registered voters, what is the approximate probability that a. At least 150 favor such a waiting perio
> Seventy percent of the bicycles sold by a certain store are mountain bikes. Among 100 randomly selected bike purchases, what is the approximate probability that a. At most 75 are mountain bikes? b. Between 60 and 75 (inclusive) are mountain bikes? c.
> Let x denote the IQ of an individual selected at random from a certain population. The value of x must be a whole number. Suppose that the distribution of x can be approximated by a normal distribution with mean value 100 and standard deviation 15. Appro
> The longest “run” of S’s in the 10-trial sequence SSFSSSSFFS has length 4, corresponding to the S’s on the fourth, fifth, sixth, and seventh trials. Consider a binomial experiment with n = 4, and let y be the length (number of trials) in the longest run
> A coin is flipped 25 times. Let x be the number of flips that result in heads (H). Consider the following rule for deciding whether or not the coin is fair: In this section, you will see how probabilities for some discrete random variables can be approxi
> A soft-drink machine dispenses only regular Coke and Diet Coke. Sixty percent of all purchases from this machine are diet drinks. The machine currently has 10 cans of each type. If 15 customers want to purchase drinks before the machine is restocked, wha
> Suppose that 20% of the 10,000 signatures on a certain recall petition are invalid. Would the number of invalid signatures in a sample of size 2000 have (approximately) a binomial distribution? Explain.
> You are to take a multiple-choice exam consisting of 100 questions with five possible responses to each question. Suppose that you have not studied and so must guess (randomly select one of the five answers) on each question. Let x represent the number o
> A breeder of show dogs is interested in the number of female puppies in a litter. If a birth is equally likely to result in a male or a female puppy, give the probability distribution of the variable x = number of female puppies in a litter of size 5.
> An experiment was conducted to investigate whether a graphologist (a handwriting analyst) could distinguish a normal person’s handwriting from that of a psychotic. A wellknown expert was given 10 files, each containing handwriting samples from a normal p
> Suppose that 5% of cereal boxes contain a prize and the other 95% contain the message, “Sorry, try again.” Consider the random variable x, where x 5 number of boxes purchased until a prize is found. a. What is the probability that at most two boxes must
> Sophie is a dog who loves to play catch. Unfortunately, she isn’t very good at this, and the probability that she catches a ball is only 0.1. Let x be the number of tosses required until Sophie catches a ball. a. Does x have a binomial or a geometric di
> Thirty percent of all automobiles undergoing an emissions inspection at a certain inspection station fail the inspection. a. Among 15 randomly selected cars, what is the probability that at most 5 fail the inspection? b. Among 15 randomly selected cars
> Refer to the previous exercise, and suppose that 10 rather than 6 passengers are selected (n = 10, p = 0.8). Use Appendix A Table 9 to find the following: a. p(8) b. P(x ≤ 7) c. The probability that more than half of the selected passengers travel wit
> FlightView surveyed 2600 North American airline passengers and reported that approximately 80% said that they carry a smartphone when they travel (www.flightview.com /travelersSurvey/downloads/survey_infographic_poster.pdf, retrieved may 2, 2017). Suppos
> Information Security Buzz provides news for the information security community. In an article published on September 24, 2016, it reported that based on a large international survey of Internet users, 60% of Internet users have installed security solutio
> Women’s Health Magazine surveyed 1187 readers to find out how often people wash their sheets (march 26, 2015, www.womenshealthmag.com/health/dirty-sheets, retrieved may 2, 2017). They found that even though microbiologists recommend that you wash your sh
> Suppose a playlist on an MP3 music player consisting of 100 songs includes 8 by a particular artist. Suppose that songs are played by selecting a song at random (with replacement) from the playlist. The random variable x represents the number of songs un
> Industrial quality control programs often include inspection of incoming materials from suppliers. If parts are purchased in large lots, a typical plan might be to select 20 parts at random from a lot and inspect them. Suppose that a lot is judged accept
> Twenty-five percent of the customers of a grocery store use an express checkout. Consider five randomly selected customers, and let x denote the number among the five who use the express checkout. a. Calculate p(2), that is, P(x = 2). b. Calculate P(x
> Suppose that in a certain metropolitan area, 90% of all households have cable TV. Let x denote the number among four randomly selected households that have cable TV. Then x is a binomial random variable with n = 4 and p = 0.9. a. Calculate p(2) = P(x =
> Example 6.27 described a study in which a person was asked to determine which of three t-shirts had been worn by her roommate by smelling the shirts (“Socio chemosensory and emotional Functions,” Psychological Science [2009]: 1118– 1123). Suppose that in
> Consider the following sample of 25 observations on x = diameter (in centimeters) of CD disks produced by a particular manufacturer: The 13 largest normal scores for a sample of size 25 are 1.964, 1.519, 1.259, 1.064, 0.903, 0.763, 0.636, 0.519, 0.408,
> The accompanying data on x 5 student-teacher ratio is for a random sample of 20 high schools in Maine selected from a population of 85 high schools. The data are consistent with summary values for the state of Maine that appeared in an article in the Ban
> An automobile manufacturer is interested in the fuel efficiency of a proposed new car design. Six nonprofessional drivers were selected, and each one drove a prototype of the new car from Phoenix to Los Angeles. The resulting fuel efficiencies (x, in mil
> Fat contents (x, in grams) for seven randomly selected hot dog brands that were rated as very good by consumer reports (www.consumerreports.org) are shown below. The normal scores for a sample of size 7 are a. Construct a normal probability plot for the
> Consider the following 10 observations on the lifetime (in hours) for a certain type of power supply: Construct a normal probability plot, and comment on whether it is reasonable to think that the distribution of power supply lifetime is approximately n
> The paper “risk behavior, decision making, and music genre in Adolescent males” (marshall university, may 2009) examined the effect of type of music playing and performance on a risky, decision-making task. a. Partici
> The authors of the paper “development of nutritionally At-risk young children is Predicted by malaria, Anemia, and Stunting in Pemba, Zanzibar” (The Journal of Nutrition [2009]: 763–772) studied facto
> Let x denote the duration of a randomly selected pregnancy (the time elapsed between conception and birth). Accepted values for the mean value and standards deviation of x are 266 days and 16 days, respectively. Suppose that the probability distribution
> The light bulbs used to provide exterior lighting for a large office building have an average lifetime of 700 hours. If lifetime is approximately normally distributed with a standard deviation of 50 hours, how often should all the bulbs be replaced so th
> Suppose that the pH of soil samples taken from a certain geographic region is normally distributed with a mean of 6.00 and a standard deviation of 0.10. Suppose the pH of a randomly selected soil sample from this region will be determined. a. What is th
> Suppose that your statistics professor tells you that the scores on a midterm exam were approximately normally distributed with a mean of 78 and a standard deviation of 7. The top 15% of all scores have been designated A’s. Your score is 89. Did you earn
> The Wall Street Journal (February 15, 1972) reported that General Electric was sued in Texas for sex discrimination over a minimum height requirement of 5 feet, 7 inches. The suit claimed that this restriction eliminated more than 94% of adult females fr
> A machine producing vitamin E capsules operates so that the actual amount of vitamin E in each capsule is normally distributed with a mean of 5 mg and a standard deviation of 0.05 mg. What is the probability that a randomly selected capsule contains less
> When used in a particular DVD player, the lifetime of a certain brand of battery is normally distributed with a mean value of 6 hours and a standard deviation of 0.8 hour. Suppose that two new batteries are independently selected and put into the player.
> Suppose that the amount of time spent by a statistical consultant with a client at their first meeting is a random variable that has a normal distribution with a mean value of 60 minutes and a standard deviation of 10 minutes. a. What is the probability
> Suppose that fuel efficiency (miles per gallon, mpg) for a particular car model under specified conditions is normally distributed with a mean value of 30.0 mpg and a standard deviation of 1.2 mpg. a. What is the probability that the fuel efficiency for
> A pizza company advertises that it puts 0.5 pound of real mozzarella cheese on its medium-sized pizzas. In fact, the amount of cheese on a randomly selected medium pizza is normally distributed with a mean value of 0.5 pound and a standard deviation of
> The number of vehicles leaving a highway at a certain exit during a particular time period has a distribution that is approximately normal with mean value 500 and standard deviation 75. What is the probability that the number of cars exiting during this
> The paper referenced in Example 6.24 (“estimating waste transfer Station delays using gPS,” Waste Management [2008]: 1742–1750) describing processing times for garbage trucks also provided information on processing times at a second facility. At this sec
> A machine that produces ball bearings has initially been set so that the mean diameter of the bearings it produces is 0.500 inches. A bearing is acceptable if its diameter is within 0.004 inches of this target value. Suppose, however, that the setting ha
> The paper “examining communication- and mediabased recreational Sedentary behaviors Among canadian youth: results from the comPASS Study” (Preventive Medicine [2015]: 74–80) estimated that the time spent playing video or computer games by high school boy
> The time that it takes a randomly selected job applicant to perform a certain task has a distribution that can be approximated by a normal distribution with a mean of 120 seconds and a standard deviation of 20 seconds. The fastest 10% are to be given adv
> The paper referenced in Example 6.21 suggested that a normal distribution with mean 3500 grams and standard deviation 550 grams is a reasonable model for birth weights of babies born in Canada. a. One common medical definition of a large baby is any bab
> Purchases made at small “corner stores” were studied by the authors of the paper “changes in Quantity, Spending, and nutritional characteristics of Adult, Adolescent and child urban corner Store Purchases After an environmental intervention” (Preventive
> The article “new york city’s graffiti-removal response time rises” (The Wall Street Journal, September 16, 2016, www.wsj.com/articles/new-york-citys-graffiti-removal -response-time-rises-1473287392, retrieved may 1, 2017) states that the city took an ave
> Let z denote a random variable having a normal distribution with µ = 0 and σ = 1. Determine each of the following probabilities: a. P(z < 0.10) b. P(z < 20.10) c. P(0.40 < z < 0.85) d. P(20.85 < z < 20.40) e. P(20.40 < z < 0.85) f. P(z > 21.25) g.
> Refer to the previous exercise. Suppose that there are two machines available for cutting corks. The machine described in the preceding problem produces corks with diameters that are approximately normally distributed with mean 3 cm and standard deviatio
> A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter of the corks produced is well approximated by a normal distribution with mean 3 cm and standard deviation 0.1 cm. The specifications call for corks wi
> Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using a new type of split keyboard can be approximated by a normal curve with mean 60 wpm and standard deviation 15 wpm (“the effects of Split Keyboard geomet
> Consider the population of all one-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean u = 5 ml and standard deviation σ = 0.2 ml is a reasonable model for the distribution of the varia
> Let z denote a random variable that has a standard normal distribution. Determine each of the following probabilities: a. P(z < 2.36) b. P(z ≤ 2.36) c. P(z < 21.23) d. P(1.14 < z , 3.35) e. P(20.77 ≤ z ≤ 20.55) f. P(z > 2) g. P(z ≥ 23.38) h. P(z <
> A consumer group is interested in estimating the proportion of packages of ground beef sold at a particular store that have an actual fat content exceeding the fat content stated on the label. How many packages of ground beef should be tested in order to
> The article “Kids Digital Day: Almost 8 Hours” (USA TODAY, January 20, 2010) summarized a national survey of 2002 Americans age 8 to 18. The sample was selected to be representative of Americans in this age group. a. Of those surveyed, 1321 reported own
> For the study described in the previous exercise, use the fivestep process for estimation problems (EMC3) to construct and interpret a 90% confidence interval for the proportion of adult American Internet users who use Facebook. Identify each of the five
> The study “The Demographics of Social Media Users” (Pew Research Center, August 19, 2015) reported that 72% of adult American Internet users use Facebook. The 72% figure was based on a representative sample of n = 1602 adult American Internet users. Supp
> Based on data from a survey of 1200 randomly selected Facebook users (USA TODAY, March 24, 2010), a 90% confidence interval for the proportion of all Facebook users who say it is not OK to “friend” someone who reports to you at work is (0.60, 0.64). What
> Describe how each of the following factors affects the width of the large-sample confidence interval for p: a. The confidence level b. The sample size c. The value of pˆ
> Suppose that county planners are interested in learning about the proportion of county residents who would pay a fee for a curbside recycling service if the county were to offer this service. Two different people independently selected random samples of
> In a survey on supernatural experiences, 722 of 4013 adult Americans reported that they had seen a ghost (“What Supernatural Experiences We’ve Had,” USA TODAY, February 8, 2010). Assume that this sample is representative of the population of adult Americ
> Consider taking a random sample from a population with p = 0.25. a. What is the standard error of p ˆ for random samples of size 400? b. Would the standard error of pˆ be smaller for random samples of size 200 or samples of size 400? c. Does cutting t
> In response to budget cuts, county officials are interested in learning about the proportion of county residents who favor closure of a county park rather than closure of a county library. In a random sample of 500 county residents, 198 favored closure o
> A random sample will be selected from the population of all adult residents of a particular city. The sample proportion pˆ will be used to estimate p, the proportion of all adult residents who are registered to vote. For which of the following situations
> Will pˆ from a random sample of size 400 tend to be closer to the actual value of the population proportion when p = 0.4 or when p = 0.7? Provide an explanation for your choice.
> Will pˆ from a random sample from a population with 60% successes tend to be closer to 0.6 for a sample size of n = 400 or a sample size of n = 800? Provide an explanation for your choice.
> Two statistics are being considered for estimating the value of a population characteristic. The sampling distributions of the two statistics are shown here. a. Suppose the actual value of the population characteristic is 50. Is Statistic I or Statistic
> Two statistics are being considered for estimating the value of a population characteristic. The sampling distributions of the two statistics are shown here. Explain why Statistic II would be preferred over Statistic I. - Statistic II Statistic I Val
> A 2016 study of 120 U.S. brand-name products found that 70% were active on Snapchat (June 15, 2016, www.businessinsider.com/what-exactly-are-brands-posting-on-snapchat-2016-6, retrieved May 4, 2017). The researchers conducting the study used bootstrap me
> The report titled “One in Three American Households Are Stuck in a Relationship with a Financial Services Provider They Don’t Trust” (June 29, 2016, www.businesswire.com/news /home/20160629005198/en/American-Households-Stuck -Relationship-Financial-Servi
> In mid-2016 the United Kingdom (UK) withdrew from the European Union (an event known as “Brexit”), causing economic concerns throughout the world. One indicator that economists use to monitor the health of the economy
> A survey of a representative sample of 478 U.S. employers found that 359 ranked stress as their top health and productivity concern (June 29, 2016, www.globenewswire.com/news-release/2016/06/29/852338/0/en/Seventy-five-percent-of-U-S-employers-say-stress
> During the 2016 NBA Finals, Kevin Love of the Cleveland Cavaliers successfully made 5 three-point shots out of 19 attempts. Assume that these attempts comprise a sample that is representative of his ability during the entire 2016 season. a. Explain why
> Refer to the instructions given prior to this exercise. The paper “college Students’ Social networking experiences on facebook” (Journal of Applied Developmental Psychology [2009]: 227â€
> Explain why you would not reject the null hypothesis if the P-value were 0.370.
> Explain why a P-value of 0.002 would be interpreted as strong evidence against the null hypothesis.
> For which of the following combinations of P-value and significance level would the null hypothesis be rejected? a. P-value = 0.426 = 0.05 b. P-value = 0.033 = 0.01 c. P-value = 0.046 = 0.10 d. P-value = 0.026 = 0.05 e. P-value = 0.004 = 0
> Step 5 of the five-step process for hypothesis testing is communication of results. What is involved in completing this step?
> The article “euthanasia Still acceptable to Solid majority in U.S.” (www.gallup.com, June 24, 2016, retrieved November 29, 2016) summarized data from a survey of 1025 adult Americans. When asked if doctors should be able to end a terminally ill patient’s
> For which of the following P-values will the null hypothesis be rejected when performing a test with a significance level of 0.05? a. 0.001 b. 0.021 c. 0.078 d. 0.047 e. 0.148
> Step 2 of the five-step process for hypothesis testing is selecting an appropriate method. What is involved in completing this step?
> According to a survey of a random sample of 2278 adult Americans conducted by the Harris Poll (“Do Americans prefer name brands or Store brands? well, that Depends” (theharrispoll.com, February 11, 2015, retrieved November 29, 2016), 1162 of those survey
> Use the definition of the P-value to explain the following: a. Why H0 would be rejected if P-value = 0.003 b. Why H0 would not be rejected if P-value = 0.350
> USA TODAY, (February 17, 2011) described a survey of 1008 American adults. One question on the survey asked people if they had ever sent a love letter using e-mail. Suppose that this survey used a random sample of adults and that you want to decide if th
> Every year on Groundhog Day (February 2), the famous groundhog “Punxsutawney Phil” tries to predict whether there will be 6 more weeks of winter. The article “groundhog has been off target” (USA TODAY, February 1, 2011) states that “based on weather data
> The report “robot, You can Drive my car: majority prefer Driverless technology” (transportation research institute University of michigan, www.umtri.umich.edu/what -were-doing/news/robot-you-can-drive-my-car-majority -prefer-driverless-technology, july 2
> The article “most customers oK with new bulbs” (USA TODAY, February 18, 2011) describes a survey of 1016 randomly selected adult Americans. Each person in the sample was asked if they have replaced standard light bulbs in their home with the more energy
> The paper “bedtime mobile phone Use and Sleep in adults” (Social Science and Medicine [2016]: 93–101) describes a study of 844 adults living in Belgium. Suppose that it is reasonable to regard this sample as a random sample of adults living in Belgium. Y
> In the report “healthy people 2020 objectives for the nation,” The Centers for Disease Control and Prevention (CDC) set a goal of 0.341 for the proportion of mothers who will still be breastfeeding their babies one year after birth (www.cdc.gov/breastfee
> The United States elections project (www.electproject .org/2016g, retrieved January 22, 2017) reported that 57.8% of registered voters in California voted in the 2016 presidential election and that this was less than the national percentage of 60.0%. Exp
> How accurate are DNA paternity tests? By comparing the DNA of the baby and the DNA of a man that is being tested, one maker of DNA paternity tests claims that their test is 100% accurate if the man is not the father and 99.99% accurate if the man is the
> Give an example of a situation where you would not want to select a very small significance level.
> Give an example of a situation where you would want to select a small significance level.
> Describe the two types of errors that might be made when a hypothesis test is carried out.
> Medical personnel are required to report suspected cases of child abuse. Because some diseases have symptoms that are similar to those of child abuse, doctors who see a child with these symptoms must decide between two competing hypotheses: H0: symptoms
> An automobile manufacturer is considering using robots for part of its assembly process. Converting to robots is expensive, so it will be done only if there is strong evidence that the proportion of defective installations is less for the robots than for
> A manufacturer of handheld calculators receives large shipments of printed circuits from a supplier. It is too costly and time-consuming to inspect all incoming circuits, so when each shipment arrives, a sample is selected for inspection. A shipment is d
> Suppose that for a particular hypothesis test, the consequences of a Type I error are not very serious, but there are serious consequences associated with making a Type II error. Would you want to carry out the test using a small significance level a (su
> One type of error in a hypothesis test is failing to reject a false null hypothesis. What is the other type of error that might occur when a hypothesis test is carried out?
