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, there is no predictive skill for the groundhog.” Suppose that you plan to take a random sample of 20 years and use weather data to determine the proportion of these years the groundhog’s prediction was correct. a. Describe the shape, center, and variability of the sampling distribution of p ˆ for samples of size 20 if the groundhog has only a 50–50 chance of making a correct prediction. b. Based on your answer to Part (a), what sample proportion values would convince you that the groundhog’s predictions have a better than 50–50 chance of being correct?
> 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.
> 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
> 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
> 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?
> The paper “breast mri as an adjunct to mammography for breast cancer Screening in high-risk patients” (American Journal of Roentgenology [2015]: 889–897) describes a study that investigated the useful
> A television manufacturer states that at least 90% of its TV sets will not need service during the first 3 years of operation. A consumer group wants to investigate this statement. A random sample of n = 100 purchasers is selected and each person is aske
> Occasionally, warning flares of the type contained in most automobile emergency kits fail to ignite. A consumer group wants to investigate a claim that the proportion of defective flares made by a particular manufacturer is higher than the advertised val
> Suppose that for a particular hypothesis test, the consequences of a Type I error are very serious. Would you want to carry out the test using a small significance level a (such as 0.01) or a larger significance level (such as 0.10)? Explain the reason f
> One type of error in a hypothesis test is rejecting the null hypothesis when it is true. What is the other type of error that might occur when a hypothesis test is carried out?
> A television station has been providing live coverage of a sensational criminal trial. The station’s program director wants to know if more than half of potential viewers prefer a return to regular daytime programming. A survey of randomly selected viewe
> A college has decided to introduce the use of plus and minus with letter grades, as long as there is convincing evidence that more than 60% of the faculty favor the change. A random sample of faculty will be selected, and the resulting data will be used
> Which of the following specify legitimate pairs of null and alternative hypotheses? a. H0: p = 0.25 Ha: p > 0.25 b. H0: p ( 0.40 Ha: p > 0.40 c. H0: p = 0.40 Ha: p ( 0.65 d. H0: p ≠ 0.50 Ha: p = 0.50 e. H0: p = 0.50 Ha: p > 0.50 f. H0: pˆ = 0.25 Ha
> Which of the following are legitimate hypotheses? a. p = 0.65 b. p ˆ = 0.90 c. p ˆ = 0.10 d. p = 0.45 e. p > 4.30
> In a hypothesis test, what does it mean to say that the null hypothesis was not rejected?
> A press release about a paper that appeared in The Journal of Youth and Adolescence (www.springer.com/ about1springer/media/springer1select?SgwiD50-11001-6 -1433942-0, august 26, 2013, retrieved may 8, 2017) was titled “Video games Do not make Vulnerable
> The article “public acceptability in the UK and the USa of nudging to reduce obesity: the example of reducing Sugar-Sweetened beverages” (PLOS One, June 8, 2016) describes a survey in which each person in a representative sample of 1082 adult Americans w
> The article “facebook Use and academic performance among college Students” (Computers in Human Behavior [2015]: 265–272) estimated that 87% percent of students at a large public university in California who are Facebook users update their status at least
> USA TODAY (March 4, 2010) described a survey of 1000 women age 22 to 35 who work full time. Each woman who participated in the survey was asked if she would be willing to give up some personal time in order to make more money. To determine if the resulti
> Explain why the statement pˆ >0.50 is not a legitimate hypothesis.
> In a hypothesis test, what does it mean to say that the null hypothesis was rejected?
> According to an article in Science Daily (“Sill no Strong evidence that adjunct treatment with hgh in iVf improves results,” sciencedaily.com, July 4, 2016, retrieved November 26, 2016), women who are having difficulty becoming pregnant sometimes use hum
> The article “poll finds most oppose return to Draft, wouldn’t encourage children to enlist” (associated press, December 18, 2005) reports that in a random sample of 1000 American adults, 430 answered “yes” to the following question: “If the military draf
> The article “facebook Use and academic performance among college Students,” Computers in Human Behavior [2015]: 265–272) estimated that 70% of students at a large public university in California who are Facebook users log into their Facebook profiles at
> careerbuilder.com conducted a survey to learn about the proportion of employers who perform background checks when evaluating a candidate for employment (“majority of employers background check employees...here's why,” november 17, 2016, retrieved novemb
> Explain why the statement p ˆ = 0.40 is not a legitimate hypothesis.
> Past experience is that when individuals are approached with a request to fill out and return a particular questionnaire in a provided stamped and addressed envelope, the response rate is 40%. An investigator believes that if the person distributing the
> Public Policy Polling conducts an annual poll on sportsrelated issues. In 2015, they found that in a sample of 1222 adult Americans, 794 said that they thought the designated hitter rule in professional baseball should be eliminated and that pitchers sho
> Suppose that the sample of 899 college students described in the previous exercise can be regarded as representative of college students in the United States. a. What hypotheses would you test to answer the question posed in the previous exercise? b. I
> The paper “i Smoke but i am not a Smoker” (Journal of American College Health [2010]: 117–125) describes a survey of 899 college students who were asked about their smoking behavior. Of the students s
> Refer to the instructions prior to this exercise. The article “the average american is in credit card Debt, no matter the economy” (Money, february 9, 2016) states that in 2015, the average credit card debt for America
> “most Like it hot” is the title of a press release issued by the Pew Research Center (march 18, 2009, www.pewsocialtrends. org). The press release states that “by an overwhelming margin, Americans want to live in a sunny place.” This statement is based o
> The article “cops get Screened for Digital Dirt” (USA TODAY, November 12, 2010) summarizes a report on law enforcement agency use of social media to screen applicants for employment. The report was based on a survey of 728 law enforcement agencies. One q
> Suppose that you are an inspector for the Fish and Game Department and that you are given the task of determining whether to prohibit fishing along part of the Oregon coast. You will close an area to fishing if it is determined that more than 3% of fish
> The paper “Living near nuclear power plants and thyroid cancer risks” (Environmental International [2016]: 42–48) investigated whether living near a nuclear power plant increases the risk of thyroid cancer. The authors of this paper concluded that there
> Researchers at the University of Washington and Harvard University analyzed records of breast cancer screening and diagnostic evaluations (“mammogram cancer Scares more frequent than thought,” USA TODAY, April 16, 1998). Discussing the benefits and downs
> Explain why failing to reject the null hypothesis in a hypothesis test does not mean there is convincing evidence that the null hypothesis is true.
> The article “how to block nuisance calls” (The Guardian, November 7, 2015) reported that in a survey of mobile phone users, 70% of those surveyed said they had received at least one nuisance call to their mobile phone in the last month. Suppose that this
> The report "Digital Democracy Survey” (Deloitte Development LLc, 2016, www2.deloitte.com/us/en.html, retrieved November 30, 2016) says that 69% of U.S. teens age 14 to 18 years access social media from a mobile phone. Suppose you plan to select a random
> A county commissioner must vote on a resolution that would commit substantial resources to the construction of a sewer in an outlying residential area. Her fiscal decisions have been criticized in the past, so she decides to take a survey of residents in
> At one point during the 2015 NFL season, Head Coach Bill Belichick and the New England Patriots had won 19 of their past 25 called coin flips at the beginning of NFL games (“for bill belichick, patriots’ strategy is no flip of the coin,” www.bostonglobe.
> Recall that in Exercise 10.63, a survey of 304 U.S. businesses found that 201 indicated that they monitor employees’ website visits. This data was used to determine if there is convincing evidence that a majority of businesses monitor e
